{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0001","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[0,0],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([0, 0], [[-1, 0, 0, 0, 是], [0, -1, 0, 0, 是], [1, 1, 3, 0, 是]], 是)","explanation_zh":"應用擴展核對=([0, 0], [[-1, 0, 0, 0, 是], [0, -1, 0, 0, 是], [1, 1, 3, 0, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216001,"parameters":{"point":[0,0],"constraints":[[-1,0,0],[0,-1,0],[1,1,3]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"point\":[0,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0002","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[1,1],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [[-1, 0, 0, -1, 是], [0, -1, 0, -1, 是], [1, 1, 4, 2, 是]], 是)","explanation_zh":"應用擴展核對=([1, 1], [[-1, 0, 0, -1, 是], [0, -1, 0, -1, 是], [1, 1, 4, 2, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216002,"parameters":{"point":[1,1],"constraints":[[-1,0,0],[0,-1,0],[1,1,4]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"point\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0003","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[2,2],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([2, 2], [[-1, 0, 0, -2, 是], [0, -1, 0, -2, 是], [1, 1, 5, 4, 是]], 是)","explanation_zh":"應用擴展核對=([2, 2], [[-1, 0, 0, -2, 是], [0, -1, 0, -2, 是], [1, 1, 5, 4, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216003,"parameters":{"point":[2,2],"constraints":[[-1,0,0],[0,-1,0],[1,1,5]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"point\":[2,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0004","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[3,3],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([3, 3], [[-1, 0, 0, -3, 是], [0, -1, 0, -3, 是], [1, 1, 6, 6, 是]], 是)","explanation_zh":"應用擴展核對=([3, 3], [[-1, 0, 0, -3, 是], [0, -1, 0, -3, 是], [1, 1, 6, 6, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216004,"parameters":{"point":[3,3],"constraints":[[-1,0,0],[0,-1,0],[1,1,6]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"point\":[3,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0005","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[4,0],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([4, 0], [[-1, 0, 0, -4, 是], [0, -1, 0, 0, 是], [1, 1, 7, 4, 是]], 是)","explanation_zh":"應用擴展核對=([4, 0], [[-1, 0, 0, -4, 是], [0, -1, 0, 0, 是], [1, 1, 7, 4, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216005,"parameters":{"point":[4,0],"constraints":[[-1,0,0],[0,-1,0],[1,1,7]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]],\"point\":[4,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0006","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[0,1],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [[-1, 0, 0, 0, 是], [0, -1, 0, -1, 是], [1, 1, 8, 1, 是]], 是)","explanation_zh":"應用擴展核對=([0, 1], [[-1, 0, 0, 0, 是], [0, -1, 0, -1, 是], [1, 1, 8, 1, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216006,"parameters":{"point":[0,1],"constraints":[[-1,0,0],[0,-1,0],[1,1,8]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]],\"point\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0007","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[1,2],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [[-1, 0, 0, -1, 是], [0, -1, 0, -2, 是], [1, 1, 9, 3, 是]], 是)","explanation_zh":"應用擴展核對=([1, 2], [[-1, 0, 0, -1, 是], [0, -1, 0, -2, 是], [1, 1, 9, 3, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216007,"parameters":{"point":[1,2],"constraints":[[-1,0,0],[0,-1,0],[1,1,9]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]],\"point\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0008","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[2,3],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [[-1, 0, 0, -2, 是], [0, -1, 0, -3, 是], [1, 1, 3, 5, 否]], 否)","explanation_zh":"應用擴展核對=([2, 3], [[-1, 0, 0, -2, 是], [0, -1, 0, -3, 是], [1, 1, 3, 5, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216008,"parameters":{"point":[2,3],"constraints":[[-1,0,0],[0,-1,0],[1,1,3]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"point\":[2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0009","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[3,0],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], [[-1, 0, 0, -3, 是], [0, -1, 0, 0, 是], [1, 1, 4, 3, 是]], 是)","explanation_zh":"應用擴展核對=([3, 0], [[-1, 0, 0, -3, 是], [0, -1, 0, 0, 是], [1, 1, 4, 3, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216009,"parameters":{"point":[3,0],"constraints":[[-1,0,0],[0,-1,0],[1,1,4]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"point\":[3,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0010","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[4,1],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([4, 1], [[-1, 0, 0, -4, 是], [0, -1, 0, -1, 是], [1, 1, 5, 5, 是]], 是)","explanation_zh":"應用擴展核對=([4, 1], [[-1, 0, 0, -4, 是], [0, -1, 0, -1, 是], [1, 1, 5, 5, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216010,"parameters":{"point":[4,1],"constraints":[[-1,0,0],[0,-1,0],[1,1,5]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"point\":[4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0011","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[0,2],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[-1, 0, 0, 0, 是], [0, -1, 0, -2, 是], [1, 1, 6, 2, 是]], 是)","explanation_zh":"應用擴展核對=([0, 2], [[-1, 0, 0, 0, 是], [0, -1, 0, -2, 是], [1, 1, 6, 2, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216011,"parameters":{"point":[0,2],"constraints":[[-1,0,0],[0,-1,0],[1,1,6]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"point\":[0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0012","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[1,3],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [[-1, 0, 0, -1, 是], [0, -1, 0, -3, 是], [1, 1, 7, 4, 是]], 是)","explanation_zh":"應用擴展核對=([1, 3], [[-1, 0, 0, -1, 是], [0, -1, 0, -3, 是], [1, 1, 7, 4, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216012,"parameters":{"point":[1,3],"constraints":[[-1,0,0],[0,-1,0],[1,1,7]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]],\"point\":[1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0013","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[2,0],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([2, 0], [[-1, 0, 0, -2, 是], [0, -1, 0, 0, 是], [1, 1, 8, 2, 是]], 是)","explanation_zh":"應用擴展核對=([2, 0], [[-1, 0, 0, -2, 是], [0, -1, 0, 0, 是], [1, 1, 8, 2, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216013,"parameters":{"point":[2,0],"constraints":[[-1,0,0],[0,-1,0],[1,1,8]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]],\"point\":[2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0014","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[3,1],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([3, 1], [[-1, 0, 0, -3, 是], [0, -1, 0, -1, 是], [1, 1, 9, 4, 是]], 是)","explanation_zh":"應用擴展核對=([3, 1], [[-1, 0, 0, -3, 是], [0, -1, 0, -1, 是], [1, 1, 9, 4, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216014,"parameters":{"point":[3,1],"constraints":[[-1,0,0],[0,-1,0],[1,1,9]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]],\"point\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0015","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[4,2],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([4, 2], [[-1, 0, 0, -4, 是], [0, -1, 0, -2, 是], [1, 1, 3, 6, 否]], 否)","explanation_zh":"應用擴展核對=([4, 2], [[-1, 0, 0, -4, 是], [0, -1, 0, -2, 是], [1, 1, 3, 6, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216015,"parameters":{"point":[4,2],"constraints":[[-1,0,0],[0,-1,0],[1,1,3]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"point\":[4,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0016","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[0,3],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([0, 3], [[-1, 0, 0, 0, 是], [0, -1, 0, -3, 是], [1, 1, 4, 3, 是]], 是)","explanation_zh":"應用擴展核對=([0, 3], [[-1, 0, 0, 0, 是], [0, -1, 0, -3, 是], [1, 1, 4, 3, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216016,"parameters":{"point":[0,3],"constraints":[[-1,0,0],[0,-1,0],[1,1,4]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"point\":[0,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0017","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[1,0],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([1, 0], [[-1, 0, 0, -1, 是], [0, -1, 0, 0, 是], [1, 1, 5, 1, 是]], 是)","explanation_zh":"應用擴展核對=([1, 0], [[-1, 0, 0, -1, 是], [0, -1, 0, 0, 是], [1, 1, 5, 1, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216017,"parameters":{"point":[1,0],"constraints":[[-1,0,0],[0,-1,0],[1,1,5]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"point\":[1,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0018","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[2,1],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([2, 1], [[-1, 0, 0, -2, 是], [0, -1, 0, -1, 是], [1, 1, 6, 3, 是]], 是)","explanation_zh":"應用擴展核對=([2, 1], [[-1, 0, 0, -2, 是], [0, -1, 0, -1, 是], [1, 1, 6, 3, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216018,"parameters":{"point":[2,1],"constraints":[[-1,0,0],[0,-1,0],[1,1,6]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"point\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0019","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[3,2],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([3, 2], [[-1, 0, 0, -3, 是], [0, -1, 0, -2, 是], [1, 1, 7, 5, 是]], 是)","explanation_zh":"應用擴展核對=([3, 2], [[-1, 0, 0, -3, 是], [0, -1, 0, -2, 是], [1, 1, 7, 5, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216019,"parameters":{"point":[3,2],"constraints":[[-1,0,0],[0,-1,0],[1,1,7]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]],\"point\":[3,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0020","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[4,3],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([4, 3], [[-1, 0, 0, -4, 是], [0, -1, 0, -3, 是], [1, 1, 8, 7, 是]], 是)","explanation_zh":"應用擴展核對=([4, 3], [[-1, 0, 0, -4, 是], [0, -1, 0, -3, 是], [1, 1, 8, 7, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216020,"parameters":{"point":[4,3],"constraints":[[-1,0,0],[0,-1,0],[1,1,8]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]],\"point\":[4,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0021","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[0,0],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([0, 0], [[-1, 0, 0, 0, 是], [0, -1, 0, 0, 是], [1, 1, 9, 0, 是]], 是)","explanation_zh":"應用擴展核對=([0, 0], [[-1, 0, 0, 0, 是], [0, -1, 0, 0, 是], [1, 1, 9, 0, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216021,"parameters":{"point":[0,0],"constraints":[[-1,0,0],[0,-1,0],[1,1,9]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]],\"point\":[0,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0022","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[1,1],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([1, 1], [[-1, 0, 0, -1, 是], [0, -1, 0, -1, 是], [1, 1, 3, 2, 是]], 是)","explanation_zh":"應用擴展核對=([1, 1], [[-1, 0, 0, -1, 是], [0, -1, 0, -1, 是], [1, 1, 3, 2, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216022,"parameters":{"point":[1,1],"constraints":[[-1,0,0],[0,-1,0],[1,1,3]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"point\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0023","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[2,2],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([2, 2], [[-1, 0, 0, -2, 是], [0, -1, 0, -2, 是], [1, 1, 4, 4, 是]], 是)","explanation_zh":"應用擴展核對=([2, 2], [[-1, 0, 0, -2, 是], [0, -1, 0, -2, 是], [1, 1, 4, 4, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216023,"parameters":{"point":[2,2],"constraints":[[-1,0,0],[0,-1,0],[1,1,4]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"point\":[2,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0024","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[3,3],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([3, 3], [[-1, 0, 0, -3, 是], [0, -1, 0, -3, 是], [1, 1, 5, 6, 否]], 否)","explanation_zh":"應用擴展核對=([3, 3], [[-1, 0, 0, -3, 是], [0, -1, 0, -3, 是], [1, 1, 5, 6, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216024,"parameters":{"point":[3,3],"constraints":[[-1,0,0],[0,-1,0],[1,1,5]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"point\":[3,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0025","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-constraint-row-audit；資料={\"point\":[4,0],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]]}。請依 [point,constraint_rows,feasible] 欄序回答。","answer":{"kind":"expression","value":"([4, 0], [[-1, 0, 0, -4, 是], [0, -1, 0, 0, 是], [1, 1, 6, 4, 是]], 是)","explanation_zh":"應用擴展核對=([4, 0], [[-1, 0, 0, -4, 是], [0, -1, 0, 0, 是], [1, 1, 6, 4, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-constraint-row-audit","seed":202610216025,"parameters":{"point":[4,0],"constraints":[[-1,0,0],[0,-1,0],[1,1,6]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-constraint-row-audit","semantic_template":"qf-app21-lp-constraint-row-audit/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"point\":[4,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0026","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,0],[2,0],[0,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 0, 2, [是, 是, 是], 是, null], [2, 1, 0, [是, 是, 是], 是, null], [3, 2, 0, [是, 是, 是], 是, null]], [0, 1, 2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 0, 2, [是, 是, 是], 是, null], [2, 1, 0, [是, 是, 是], 是, null], [3, 2, 0, [是, 是, 是], 是, null]], [0, 1, 2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216026,"parameters":{"points":[[0,0],[1,0],[2,0],[0,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,3]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"points\":[[0,0],[0,2],[1,0],[2,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0027","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,1],[2,1],[1,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 1, [是, 是, 是], 是, null], [2, 1, 2, [是, 是, 是], 是, null], [3, 2, 1, [是, 是, 是], 是, null]], [0, 1, 2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 1, [是, 是, 是], 是, null], [2, 1, 2, [是, 是, 是], 是, null], [3, 2, 1, [是, 是, 是], 是, null]], [0, 1, 2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216027,"parameters":{"points":[[0,0],[1,1],[2,1],[1,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,4]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"points\":[[0,0],[1,1],[1,2],[2,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0028","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,2],[2,2],[2,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 2, [是, 是, 是], 是, null], [2, 2, 2, [是, 是, 是], 是, null]], [0, 1, 2])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 2, [是, 是, 是], 是, null], [2, 2, 2, [是, 是, 是], 是, null]], [0, 1, 2])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216028,"parameters":{"points":[[0,0],[1,2],[2,2],[2,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,5]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"points\":[[0,0],[1,2],[2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0029","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,3],[2,3],[3,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 3, [是, 是, 是], 是, null], [2, 2, 3, [是, 是, 是], 是, null], [3, 3, 2, [是, 是, 是], 是, null]], [0, 1, 2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 3, [是, 是, 是], 是, null], [2, 2, 3, [是, 是, 是], 是, null], [3, 3, 2, [是, 是, 是], 是, null]], [0, 1, 2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216029,"parameters":{"points":[[0,0],[1,3],[2,3],[3,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,6]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"points\":[[0,0],[1,3],[2,3],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0030","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,0],[2,4],[4,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 0, [是, 是, 是], 是, null], [2, 2, 4, [是, 是, 是], 是, null], [3, 4, 2, [是, 是, 是], 是, null]], [0, 1, 2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 0, [是, 是, 是], 是, null], [2, 2, 4, [是, 是, 是], 是, null], [3, 4, 2, [是, 是, 是], 是, null]], [0, 1, 2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216030,"parameters":{"points":[[0,0],[1,0],[2,4],[4,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,7]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]],\"points\":[[0,0],[1,0],[2,4],[4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0031","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,1],[2,0],[5,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 1, [是, 是, 是], 是, null], [2, 2, 0, [是, 是, 是], 是, null], [3, 5, 2, [是, 是, 是], 是, null]], [0, 1, 2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 1, [是, 是, 是], 是, null], [2, 2, 0, [是, 是, 是], 是, null], [3, 5, 2, [是, 是, 是], 是, null]], [0, 1, 2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216031,"parameters":{"points":[[0,0],[1,1],[2,0],[5,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,8]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]],\"points\":[[0,0],[1,1],[2,0],[5,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0032","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,2],[2,1],[0,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 0, 2, [是, 是, 是], 是, null], [2, 1, 2, [是, 是, 是], 是, null], [3, 2, 1, [是, 是, 是], 是, null]], [0, 1, 2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 0, 2, [是, 是, 是], 是, null], [2, 1, 2, [是, 是, 是], 是, null], [3, 2, 1, [是, 是, 是], 是, null]], [0, 1, 2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216032,"parameters":{"points":[[0,0],[1,2],[2,1],[0,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,9]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]],\"points\":[[0,0],[0,2],[1,2],[2,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0033","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,3],[2,2],[1,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 2, [是, 是, 是], 是, null], [2, 1, 3, [是, 是, 否], 否, null], [3, 2, 2, [是, 是, 否], 否, null]], [0, 1])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 2, [是, 是, 是], 是, null], [2, 1, 3, [是, 是, 否], 否, null], [3, 2, 2, [是, 是, 否], 否, null]], [0, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216033,"parameters":{"points":[[0,0],[1,3],[2,2],[1,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,3]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"points\":[[0,0],[1,2],[1,3],[2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0034","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,0],[2,3],[2,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 0, [是, 是, 是], 是, null], [2, 2, 2, [是, 是, 是], 是, null], [3, 2, 3, [是, 是, 否], 否, null]], [0, 1, 2])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 0, [是, 是, 是], 是, null], [2, 2, 2, [是, 是, 是], 是, null], [3, 2, 3, [是, 是, 否], 否, null]], [0, 1, 2])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216034,"parameters":{"points":[[0,0],[1,0],[2,3],[2,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,4]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"points\":[[0,0],[1,0],[2,2],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0035","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,1],[2,4],[3,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 1, [是, 是, 是], 是, null], [2, 2, 4, [是, 是, 否], 否, null], [3, 3, 2, [是, 是, 是], 是, null]], [0, 1, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 1, [是, 是, 是], 是, null], [2, 2, 4, [是, 是, 否], 否, null], [3, 3, 2, [是, 是, 是], 是, null]], [0, 1, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216035,"parameters":{"points":[[0,0],[1,1],[2,4],[3,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,5]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"points\":[[0,0],[1,1],[2,4],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0036","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,2],[2,0],[4,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 2, [是, 是, 是], 是, null], [2, 2, 0, [是, 是, 是], 是, null], [3, 4, 2, [是, 是, 是], 是, null]], [0, 1, 2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 2, [是, 是, 是], 是, null], [2, 2, 0, [是, 是, 是], 是, null], [3, 4, 2, [是, 是, 是], 是, null]], [0, 1, 2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216036,"parameters":{"points":[[0,0],[1,2],[2,0],[4,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,6]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"points\":[[0,0],[1,2],[2,0],[4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0037","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,3],[2,1],[5,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 3, [是, 是, 是], 是, null], [2, 2, 1, [是, 是, 是], 是, null], [3, 5, 2, [是, 是, 是], 是, null]], [0, 1, 2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 3, [是, 是, 是], 是, null], [2, 2, 1, [是, 是, 是], 是, null], [3, 5, 2, [是, 是, 是], 是, null]], [0, 1, 2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216037,"parameters":{"points":[[0,0],[1,3],[2,1],[5,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,7]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]],\"points\":[[0,0],[1,3],[2,1],[5,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0038","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,0],[2,2],[0,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 0, 2, [是, 是, 是], 是, null], [2, 1, 0, [是, 是, 是], 是, null], [3, 2, 2, [是, 是, 是], 是, null]], [0, 1, 2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 0, 2, [是, 是, 是], 是, null], [2, 1, 0, [是, 是, 是], 是, null], [3, 2, 2, [是, 是, 是], 是, null]], [0, 1, 2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216038,"parameters":{"points":[[0,0],[1,0],[2,2],[0,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,8]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]],\"points\":[[0,0],[0,2],[1,0],[2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0039","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,1],[2,3],[1,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 1, [是, 是, 是], 是, null], [2, 1, 2, [是, 是, 是], 是, null], [3, 2, 3, [是, 是, 是], 是, null]], [0, 1, 2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 1, [是, 是, 是], 是, null], [2, 1, 2, [是, 是, 是], 是, null], [3, 2, 3, [是, 是, 是], 是, null]], [0, 1, 2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216039,"parameters":{"points":[[0,0],[1,1],[2,3],[1,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,9]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]],\"points\":[[0,0],[1,1],[1,2],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0040","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,2],[2,4],[2,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 2, [是, 是, 是], 是, null], [2, 2, 2, [是, 是, 否], 否, null], [3, 2, 4, [是, 是, 否], 否, null]], [0, 1])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 2, [是, 是, 是], 是, null], [2, 2, 2, [是, 是, 否], 否, null], [3, 2, 4, [是, 是, 否], 否, null]], [0, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216040,"parameters":{"points":[[0,0],[1,2],[2,4],[2,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,3]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"points\":[[0,0],[1,2],[2,2],[2,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0041","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,3],[2,0],[3,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 3, [是, 是, 是], 是, null], [2, 2, 0, [是, 是, 是], 是, null], [3, 3, 2, [是, 是, 否], 否, null]], [0, 1, 2])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 3, [是, 是, 是], 是, null], [2, 2, 0, [是, 是, 是], 是, null], [3, 3, 2, [是, 是, 否], 否, null]], [0, 1, 2])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216041,"parameters":{"points":[[0,0],[1,3],[2,0],[3,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,4]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"points\":[[0,0],[1,3],[2,0],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0042","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,0],[2,1],[4,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 0, [是, 是, 是], 是, null], [2, 2, 1, [是, 是, 是], 是, null], [3, 4, 2, [是, 是, 否], 否, null]], [0, 1, 2])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 0, [是, 是, 是], 是, null], [2, 2, 1, [是, 是, 是], 是, null], [3, 4, 2, [是, 是, 否], 否, null]], [0, 1, 2])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216042,"parameters":{"points":[[0,0],[1,0],[2,1],[4,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,5]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"points\":[[0,0],[1,0],[2,1],[4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0043","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,1],[2,2],[5,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 1, [是, 是, 是], 是, null], [2, 2, 2, [是, 是, 是], 是, null], [3, 5, 2, [是, 是, 否], 否, null]], [0, 1, 2])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 1, [是, 是, 是], 是, null], [2, 2, 2, [是, 是, 是], 是, null], [3, 5, 2, [是, 是, 否], 否, null]], [0, 1, 2])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216043,"parameters":{"points":[[0,0],[1,1],[2,2],[5,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,6]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"points\":[[0,0],[1,1],[2,2],[5,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0044","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,2],[2,3],[0,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 0, 2, [是, 是, 是], 是, null], [2, 1, 2, [是, 是, 是], 是, null], [3, 2, 3, [是, 是, 是], 是, null]], [0, 1, 2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 0, 2, [是, 是, 是], 是, null], [2, 1, 2, [是, 是, 是], 是, null], [3, 2, 3, [是, 是, 是], 是, null]], [0, 1, 2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216044,"parameters":{"points":[[0,0],[1,2],[2,3],[0,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,7]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]],\"points\":[[0,0],[0,2],[1,2],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0045","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,3],[2,4],[1,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 2, [是, 是, 是], 是, null], [2, 1, 3, [是, 是, 是], 是, null], [3, 2, 4, [是, 是, 是], 是, null]], [0, 1, 2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 2, [是, 是, 是], 是, null], [2, 1, 3, [是, 是, 是], 是, null], [3, 2, 4, [是, 是, 是], 是, null]], [0, 1, 2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216045,"parameters":{"points":[[0,0],[1,3],[2,4],[1,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,8]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]],\"points\":[[0,0],[1,2],[1,3],[2,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0046","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,0],[2,0],[2,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 0, [是, 是, 是], 是, null], [2, 2, 0, [是, 是, 是], 是, null], [3, 2, 2, [是, 是, 是], 是, null]], [0, 1, 2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 0, [是, 是, 是], 是, null], [2, 2, 0, [是, 是, 是], 是, null], [3, 2, 2, [是, 是, 是], 是, null]], [0, 1, 2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216046,"parameters":{"points":[[0,0],[1,0],[2,0],[2,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,9]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]],\"points\":[[0,0],[1,0],[2,0],[2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0047","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,1],[2,1],[3,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 1, [是, 是, 是], 是, null], [2, 2, 1, [是, 是, 是], 是, null], [3, 3, 2, [是, 是, 否], 否, null]], [0, 1, 2])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 1, [是, 是, 是], 是, null], [2, 2, 1, [是, 是, 是], 是, null], [3, 3, 2, [是, 是, 否], 否, null]], [0, 1, 2])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216047,"parameters":{"points":[[0,0],[1,1],[2,1],[3,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,3]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"points\":[[0,0],[1,1],[2,1],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0048","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,2],[2,2],[4,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 2, [是, 是, 是], 是, null], [2, 2, 2, [是, 是, 是], 是, null], [3, 4, 2, [是, 是, 否], 否, null]], [0, 1, 2])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 2, [是, 是, 是], 是, null], [2, 2, 2, [是, 是, 是], 是, null], [3, 4, 2, [是, 是, 否], 否, null]], [0, 1, 2])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216048,"parameters":{"points":[[0,0],[1,2],[2,2],[4,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,4]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"points\":[[0,0],[1,2],[2,2],[4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0049","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,3],[2,3],[5,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 3, [是, 是, 是], 是, null], [2, 2, 3, [是, 是, 是], 是, null], [3, 5, 2, [是, 是, 否], 否, null]], [0, 1, 2])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 1, 3, [是, 是, 是], 是, null], [2, 2, 3, [是, 是, 是], 是, null], [3, 5, 2, [是, 是, 否], 否, null]], [0, 1, 2])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216049,"parameters":{"points":[[0,0],[1,3],[2,3],[5,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,5]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"points\":[[0,0],[1,3],[2,3],[5,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0050","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-feasible-inventory；資料={\"points\":[[0,0],[1,0],[2,4],[0,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]]}。請依 [constraints,point_rows,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 0, 2, [是, 是, 是], 是, null], [2, 1, 0, [是, 是, 是], 是, null], [3, 2, 4, [是, 是, 是], 是, null]], [0, 1, 2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [[0, 0, 0, [是, 是, 是], 是, null], [1, 0, 2, [是, 是, 是], 是, null], [2, 1, 0, [是, 是, 是], 是, null], [3, 2, 4, [是, 是, 是], 是, null]], [0, 1, 2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-feasible-inventory","seed":202610216050,"parameters":{"points":[[0,0],[1,0],[2,4],[0,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,6]],"domain":"Finite_linear_program_candidate_grid","operation":"lp-feasible-inventory","semantic_template":"qf-app21-lp-feasible-inventory/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"points\":[[0,0],[0,2],[1,0],[2,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0051","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,0],[2,0],[0,2]],\"objective\":[-2,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([-2, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 0, -2], [3, 2, 0, -4]])","explanation_zh":"應用擴展核對=([-2, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 0, -2], [3, 2, 0, -4]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216051,"parameters":{"points":[[0,0],[1,0],[2,0],[0,2]],"objective":[-2,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[-2,2],\"points\":[[0,0],[0,2],[1,0],[2,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0052","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,1],[2,1],[1,2]],\"objective\":[-1,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([-1, 2], [[0, 0, 0, 0], [1, 1, 1, 1], [2, 1, 2, 3], [3, 2, 1, 0]])","explanation_zh":"應用擴展核對=([-1, 2], [[0, 0, 0, 0], [1, 1, 1, 1], [2, 1, 2, 3], [3, 2, 1, 0]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216052,"parameters":{"points":[[0,0],[1,1],[2,1],[1,2]],"objective":[-1,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[-1,2],\"points\":[[0,0],[1,1],[1,2],[2,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0053","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,2],[2,2],[2,2]],\"objective\":[0,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[0, 0, 0, 0], [1, 1, 2, 4], [2, 2, 2, 4]])","explanation_zh":"應用擴展核對=([0, 2], [[0, 0, 0, 0], [1, 1, 2, 4], [2, 2, 2, 4]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216053,"parameters":{"points":[[0,0],[1,2],[2,2],[2,2]],"objective":[0,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[0,2],\"points\":[[0,0],[1,2],[2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0054","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,3],[2,3],[3,2]],\"objective\":[1,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [[0, 0, 0, 0], [1, 1, 3, 7], [2, 2, 3, 8], [3, 3, 2, 7]])","explanation_zh":"應用擴展核對=([1, 2], [[0, 0, 0, 0], [1, 1, 3, 7], [2, 2, 3, 8], [3, 3, 2, 7]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216054,"parameters":{"points":[[0,0],[1,3],[2,3],[3,2]],"objective":[1,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,3],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0055","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,0],[2,4],[4,2]],\"objective\":[2,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([2, 2], [[0, 0, 0, 0], [1, 1, 0, 2], [2, 2, 4, 12], [3, 4, 2, 12]])","explanation_zh":"應用擴展核對=([2, 2], [[0, 0, 0, 0], [1, 1, 0, 2], [2, 2, 4, 12], [3, 4, 2, 12]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216055,"parameters":{"points":[[0,0],[1,0],[2,4],[4,2]],"objective":[2,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[2,2],\"points\":[[0,0],[1,0],[2,4],[4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0056","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,1],[2,0],[5,2]],\"objective\":[-2,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([-2, 2], [[0, 0, 0, 0], [1, 1, 1, 0], [2, 2, 0, -4], [3, 5, 2, -6]])","explanation_zh":"應用擴展核對=([-2, 2], [[0, 0, 0, 0], [1, 1, 1, 0], [2, 2, 0, -4], [3, 5, 2, -6]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216056,"parameters":{"points":[[0,0],[1,1],[2,0],[5,2]],"objective":[-2,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[-2,2],\"points\":[[0,0],[1,1],[2,0],[5,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0057","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,2],[2,1],[0,2]],\"objective\":[-1,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([-1, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 2, 3], [3, 2, 1, 0]])","explanation_zh":"應用擴展核對=([-1, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 2, 3], [3, 2, 1, 0]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216057,"parameters":{"points":[[0,0],[1,2],[2,1],[0,2]],"objective":[-1,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[-1,2],\"points\":[[0,0],[0,2],[1,2],[2,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0058","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,3],[2,2],[1,2]],\"objective\":[0,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[0, 0, 0, 0], [1, 1, 2, 4], [2, 1, 3, 6], [3, 2, 2, 4]])","explanation_zh":"應用擴展核對=([0, 2], [[0, 0, 0, 0], [1, 1, 2, 4], [2, 1, 3, 6], [3, 2, 2, 4]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216058,"parameters":{"points":[[0,0],[1,3],[2,2],[1,2]],"objective":[0,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[0,2],\"points\":[[0,0],[1,2],[1,3],[2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0059","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,0],[2,3],[2,2]],\"objective\":[1,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [[0, 0, 0, 0], [1, 1, 0, 1], [2, 2, 2, 6], [3, 2, 3, 8]])","explanation_zh":"應用擴展核對=([1, 2], [[0, 0, 0, 0], [1, 1, 0, 1], [2, 2, 2, 6], [3, 2, 3, 8]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216059,"parameters":{"points":[[0,0],[1,0],[2,3],[2,2]],"objective":[1,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[1,2],\"points\":[[0,0],[1,0],[2,2],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0060","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,1],[2,4],[3,2]],\"objective\":[2,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([2, 2], [[0, 0, 0, 0], [1, 1, 1, 4], [2, 2, 4, 12], [3, 3, 2, 10]])","explanation_zh":"應用擴展核對=([2, 2], [[0, 0, 0, 0], [1, 1, 1, 4], [2, 2, 4, 12], [3, 3, 2, 10]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216060,"parameters":{"points":[[0,0],[1,1],[2,4],[3,2]],"objective":[2,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[2,2],\"points\":[[0,0],[1,1],[2,4],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0061","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,2],[2,0],[4,2]],\"objective\":[-2,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([-2, 2], [[0, 0, 0, 0], [1, 1, 2, 2], [2, 2, 0, -4], [3, 4, 2, -4]])","explanation_zh":"應用擴展核對=([-2, 2], [[0, 0, 0, 0], [1, 1, 2, 2], [2, 2, 0, -4], [3, 4, 2, -4]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216061,"parameters":{"points":[[0,0],[1,2],[2,0],[4,2]],"objective":[-2,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[-2,2],\"points\":[[0,0],[1,2],[2,0],[4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0062","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,3],[2,1],[5,2]],\"objective\":[-1,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([-1, 2], [[0, 0, 0, 0], [1, 1, 3, 5], [2, 2, 1, 0], [3, 5, 2, -1]])","explanation_zh":"應用擴展核對=([-1, 2], [[0, 0, 0, 0], [1, 1, 3, 5], [2, 2, 1, 0], [3, 5, 2, -1]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216062,"parameters":{"points":[[0,0],[1,3],[2,1],[5,2]],"objective":[-1,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[-1,2],\"points\":[[0,0],[1,3],[2,1],[5,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0063","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,0],[2,2],[0,2]],\"objective\":[0,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 0, 0], [3, 2, 2, 4]])","explanation_zh":"應用擴展核對=([0, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 0, 0], [3, 2, 2, 4]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216063,"parameters":{"points":[[0,0],[1,0],[2,2],[0,2]],"objective":[0,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[0,2],\"points\":[[0,0],[0,2],[1,0],[2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0064","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,1],[2,3],[1,2]],\"objective\":[1,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [[0, 0, 0, 0], [1, 1, 1, 3], [2, 1, 2, 5], [3, 2, 3, 8]])","explanation_zh":"應用擴展核對=([1, 2], [[0, 0, 0, 0], [1, 1, 1, 3], [2, 1, 2, 5], [3, 2, 3, 8]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216064,"parameters":{"points":[[0,0],[1,1],[2,3],[1,2]],"objective":[1,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[1,2],\"points\":[[0,0],[1,1],[1,2],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0065","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,2],[2,4],[2,2]],\"objective\":[2,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([2, 2], [[0, 0, 0, 0], [1, 1, 2, 6], [2, 2, 2, 8], [3, 2, 4, 12]])","explanation_zh":"應用擴展核對=([2, 2], [[0, 0, 0, 0], [1, 1, 2, 6], [2, 2, 2, 8], [3, 2, 4, 12]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216065,"parameters":{"points":[[0,0],[1,2],[2,4],[2,2]],"objective":[2,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[2,2],\"points\":[[0,0],[1,2],[2,2],[2,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0066","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,3],[2,0],[3,2]],\"objective\":[-2,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([-2, 2], [[0, 0, 0, 0], [1, 1, 3, 4], [2, 2, 0, -4], [3, 3, 2, -2]])","explanation_zh":"應用擴展核對=([-2, 2], [[0, 0, 0, 0], [1, 1, 3, 4], [2, 2, 0, -4], [3, 3, 2, -2]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216066,"parameters":{"points":[[0,0],[1,3],[2,0],[3,2]],"objective":[-2,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[-2,2],\"points\":[[0,0],[1,3],[2,0],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0067","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,0],[2,1],[4,2]],\"objective\":[-1,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([-1, 2], [[0, 0, 0, 0], [1, 1, 0, -1], [2, 2, 1, 0], [3, 4, 2, 0]])","explanation_zh":"應用擴展核對=([-1, 2], [[0, 0, 0, 0], [1, 1, 0, -1], [2, 2, 1, 0], [3, 4, 2, 0]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216067,"parameters":{"points":[[0,0],[1,0],[2,1],[4,2]],"objective":[-1,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[-1,2],\"points\":[[0,0],[1,0],[2,1],[4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0068","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,1],[2,2],[5,2]],\"objective\":[0,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[0, 0, 0, 0], [1, 1, 1, 2], [2, 2, 2, 4], [3, 5, 2, 4]])","explanation_zh":"應用擴展核對=([0, 2], [[0, 0, 0, 0], [1, 1, 1, 2], [2, 2, 2, 4], [3, 5, 2, 4]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216068,"parameters":{"points":[[0,0],[1,1],[2,2],[5,2]],"objective":[0,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[0,2],\"points\":[[0,0],[1,1],[2,2],[5,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0069","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,2],[2,3],[0,2]],\"objective\":[1,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 2, 5], [3, 2, 3, 8]])","explanation_zh":"應用擴展核對=([1, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 2, 5], [3, 2, 3, 8]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216069,"parameters":{"points":[[0,0],[1,2],[2,3],[0,2]],"objective":[1,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[1,2],\"points\":[[0,0],[0,2],[1,2],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0070","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,3],[2,4],[1,2]],\"objective\":[2,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([2, 2], [[0, 0, 0, 0], [1, 1, 2, 6], [2, 1, 3, 8], [3, 2, 4, 12]])","explanation_zh":"應用擴展核對=([2, 2], [[0, 0, 0, 0], [1, 1, 2, 6], [2, 1, 3, 8], [3, 2, 4, 12]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216070,"parameters":{"points":[[0,0],[1,3],[2,4],[1,2]],"objective":[2,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[2,2],\"points\":[[0,0],[1,2],[1,3],[2,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0071","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,0],[2,0],[2,2]],\"objective\":[-2,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([-2, 2], [[0, 0, 0, 0], [1, 1, 0, -2], [2, 2, 0, -4], [3, 2, 2, 0]])","explanation_zh":"應用擴展核對=([-2, 2], [[0, 0, 0, 0], [1, 1, 0, -2], [2, 2, 0, -4], [3, 2, 2, 0]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216071,"parameters":{"points":[[0,0],[1,0],[2,0],[2,2]],"objective":[-2,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[-2,2],\"points\":[[0,0],[1,0],[2,0],[2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0072","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,1],[2,1],[3,2]],\"objective\":[-1,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([-1, 2], [[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 0], [3, 3, 2, 1]])","explanation_zh":"應用擴展核對=([-1, 2], [[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 0], [3, 3, 2, 1]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216072,"parameters":{"points":[[0,0],[1,1],[2,1],[3,2]],"objective":[-1,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[-1,2],\"points\":[[0,0],[1,1],[2,1],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0073","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,2],[2,2],[4,2]],\"objective\":[0,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[0, 0, 0, 0], [1, 1, 2, 4], [2, 2, 2, 4], [3, 4, 2, 4]])","explanation_zh":"應用擴展核對=([0, 2], [[0, 0, 0, 0], [1, 1, 2, 4], [2, 2, 2, 4], [3, 4, 2, 4]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216073,"parameters":{"points":[[0,0],[1,2],[2,2],[4,2]],"objective":[0,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[0,2],\"points\":[[0,0],[1,2],[2,2],[4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0074","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,3],[2,3],[5,2]],\"objective\":[1,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [[0, 0, 0, 0], [1, 1, 3, 7], [2, 2, 3, 8], [3, 5, 2, 9]])","explanation_zh":"應用擴展核對=([1, 2], [[0, 0, 0, 0], [1, 1, 3, 7], [2, 2, 3, 8], [3, 5, 2, 9]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216074,"parameters":{"points":[[0,0],[1,3],[2,3],[5,2]],"objective":[1,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,3],[5,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0075","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-objective-audit；資料={\"points\":[[0,0],[1,0],[2,4],[0,2]],\"objective\":[2,2]}。請依 [objective,objective_rows] 欄序回答。","answer":{"kind":"expression","value":"([2, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 0, 2], [3, 2, 4, 12]])","explanation_zh":"應用擴展核對=([2, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 0, 2], [3, 2, 4, 12]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-objective-audit","seed":202610216075,"parameters":{"points":[[0,0],[1,0],[2,4],[0,2]],"objective":[2,2],"domain":"Finite_linear_program_candidate_grid","operation":"lp-objective-audit","semantic_template":"qf-app21-lp-objective-audit/{\"objective\":[2,2],\"points\":[[0,0],[0,2],[1,0],[2,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0076","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,0],[2,0],[0,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"objective\":[-2,2],\"direction\":\"max\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [-2, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 0, 2, [是, 是, 是], 是, 4], [2, 1, 0, [是, 是, 是], 是, -2], [3, 2, 0, [是, 是, 是], 是, -4]], 4, [1])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [-2, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 0, 2, [是, 是, 是], 是, 4], [2, 1, 0, [是, 是, 是], 是, -2], [3, 2, 0, [是, 是, 是], 是, -4]], 4, [1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216076,"parameters":{"points":[[0,0],[1,0],[2,0],[0,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,3]],"objective":[-2,2],"direction":"max","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"direction\":\"max\",\"objective\":[-2,2],\"points\":[[0,0],[0,2],[1,0],[2,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0077","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,1],[2,1],[1,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"objective\":[-1,2],\"direction\":\"min\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [-1, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 1, [是, 是, 是], 是, 1], [2, 1, 2, [是, 是, 是], 是, 3], [3, 2, 1, [是, 是, 是], 是, 0]], 0, [0, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [-1, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 1, [是, 是, 是], 是, 1], [2, 1, 2, [是, 是, 是], 是, 3], [3, 2, 1, [是, 是, 是], 是, 0]], 0, [0, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216077,"parameters":{"points":[[0,0],[1,1],[2,1],[1,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,4]],"objective":[-1,2],"direction":"min","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"direction\":\"min\",\"objective\":[-1,2],\"points\":[[0,0],[1,1],[1,2],[2,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0078","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,2],[2,2],[2,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"objective\":[0,2],\"direction\":\"max\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [0, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 2, [是, 是, 是], 是, 4], [2, 2, 2, [是, 是, 是], 是, 4]], 4, [1, 2])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [0, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 2, [是, 是, 是], 是, 4], [2, 2, 2, [是, 是, 是], 是, 4]], 4, [1, 2])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216078,"parameters":{"points":[[0,0],[1,2],[2,2],[2,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,5]],"objective":[0,2],"direction":"max","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"direction\":\"max\",\"objective\":[0,2],\"points\":[[0,0],[1,2],[2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0079","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,3],[2,3],[3,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"objective\":[1,2],\"direction\":\"min\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [1, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 3, [是, 是, 是], 是, 7], [2, 2, 3, [是, 是, 是], 是, 8], [3, 3, 2, [是, 是, 是], 是, 7]], 0, [0])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [1, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 3, [是, 是, 是], 是, 7], [2, 2, 3, [是, 是, 是], 是, 8], [3, 3, 2, [是, 是, 是], 是, 7]], 0, [0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216079,"parameters":{"points":[[0,0],[1,3],[2,3],[3,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,6]],"objective":[1,2],"direction":"min","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"direction\":\"min\",\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,3],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0080","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,0],[2,4],[4,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]],\"objective\":[2,2],\"direction\":\"max\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [2, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 0, [是, 是, 是], 是, 2], [2, 2, 4, [是, 是, 是], 是, 12], [3, 4, 2, [是, 是, 是], 是, 12]], 12, [2, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [2, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 0, [是, 是, 是], 是, 2], [2, 2, 4, [是, 是, 是], 是, 12], [3, 4, 2, [是, 是, 是], 是, 12]], 12, [2, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216080,"parameters":{"points":[[0,0],[1,0],[2,4],[4,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,7]],"objective":[2,2],"direction":"max","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]],\"direction\":\"max\",\"objective\":[2,2],\"points\":[[0,0],[1,0],[2,4],[4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0081","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,1],[2,0],[5,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]],\"objective\":[-2,2],\"direction\":\"min\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [-2, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 1, [是, 是, 是], 是, 0], [2, 2, 0, [是, 是, 是], 是, -4], [3, 5, 2, [是, 是, 是], 是, -6]], -6, [3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [-2, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 1, [是, 是, 是], 是, 0], [2, 2, 0, [是, 是, 是], 是, -4], [3, 5, 2, [是, 是, 是], 是, -6]], -6, [3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216081,"parameters":{"points":[[0,0],[1,1],[2,0],[5,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,8]],"objective":[-2,2],"direction":"min","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]],\"direction\":\"min\",\"objective\":[-2,2],\"points\":[[0,0],[1,1],[2,0],[5,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0082","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,2],[2,1],[0,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]],\"objective\":[-1,2],\"direction\":\"max\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [-1, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 0, 2, [是, 是, 是], 是, 4], [2, 1, 2, [是, 是, 是], 是, 3], [3, 2, 1, [是, 是, 是], 是, 0]], 4, [1])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [-1, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 0, 2, [是, 是, 是], 是, 4], [2, 1, 2, [是, 是, 是], 是, 3], [3, 2, 1, [是, 是, 是], 是, 0]], 4, [1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216082,"parameters":{"points":[[0,0],[1,2],[2,1],[0,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,9]],"objective":[-1,2],"direction":"max","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]],\"direction\":\"max\",\"objective\":[-1,2],\"points\":[[0,0],[0,2],[1,2],[2,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0083","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,3],[2,2],[1,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"objective\":[0,2],\"direction\":\"min\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [0, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 2, [是, 是, 是], 是, 4], [2, 1, 3, [是, 是, 否], 否, 6], [3, 2, 2, [是, 是, 否], 否, 4]], 0, [0])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [0, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 2, [是, 是, 是], 是, 4], [2, 1, 3, [是, 是, 否], 否, 6], [3, 2, 2, [是, 是, 否], 否, 4]], 0, [0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216083,"parameters":{"points":[[0,0],[1,3],[2,2],[1,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,3]],"objective":[0,2],"direction":"min","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"direction\":\"min\",\"objective\":[0,2],\"points\":[[0,0],[1,2],[1,3],[2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0084","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,0],[2,3],[2,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"objective\":[1,2],\"direction\":\"max\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [1, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 0, [是, 是, 是], 是, 1], [2, 2, 2, [是, 是, 是], 是, 6], [3, 2, 3, [是, 是, 否], 否, 8]], 6, [2])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [1, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 0, [是, 是, 是], 是, 1], [2, 2, 2, [是, 是, 是], 是, 6], [3, 2, 3, [是, 是, 否], 否, 8]], 6, [2])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216084,"parameters":{"points":[[0,0],[1,0],[2,3],[2,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,4]],"objective":[1,2],"direction":"max","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"direction\":\"max\",\"objective\":[1,2],\"points\":[[0,0],[1,0],[2,2],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0085","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,1],[2,4],[3,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"objective\":[2,2],\"direction\":\"min\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [2, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 1, [是, 是, 是], 是, 4], [2, 2, 4, [是, 是, 否], 否, 12], [3, 3, 2, [是, 是, 是], 是, 10]], 0, [0])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [2, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 1, [是, 是, 是], 是, 4], [2, 2, 4, [是, 是, 否], 否, 12], [3, 3, 2, [是, 是, 是], 是, 10]], 0, [0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216085,"parameters":{"points":[[0,0],[1,1],[2,4],[3,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,5]],"objective":[2,2],"direction":"min","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"direction\":\"min\",\"objective\":[2,2],\"points\":[[0,0],[1,1],[2,4],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0086","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,2],[2,0],[4,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"objective\":[-2,2],\"direction\":\"max\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [-2, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 2, [是, 是, 是], 是, 2], [2, 2, 0, [是, 是, 是], 是, -4], [3, 4, 2, [是, 是, 是], 是, -4]], 2, [1])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [-2, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 2, [是, 是, 是], 是, 2], [2, 2, 0, [是, 是, 是], 是, -4], [3, 4, 2, [是, 是, 是], 是, -4]], 2, [1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216086,"parameters":{"points":[[0,0],[1,2],[2,0],[4,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,6]],"objective":[-2,2],"direction":"max","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"direction\":\"max\",\"objective\":[-2,2],\"points\":[[0,0],[1,2],[2,0],[4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0087","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,3],[2,1],[5,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]],\"objective\":[-1,2],\"direction\":\"min\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [-1, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 3, [是, 是, 是], 是, 5], [2, 2, 1, [是, 是, 是], 是, 0], [3, 5, 2, [是, 是, 是], 是, -1]], -1, [3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [-1, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 3, [是, 是, 是], 是, 5], [2, 2, 1, [是, 是, 是], 是, 0], [3, 5, 2, [是, 是, 是], 是, -1]], -1, [3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216087,"parameters":{"points":[[0,0],[1,3],[2,1],[5,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,7]],"objective":[-1,2],"direction":"min","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]],\"direction\":\"min\",\"objective\":[-1,2],\"points\":[[0,0],[1,3],[2,1],[5,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0088","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,0],[2,2],[0,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]],\"objective\":[0,2],\"direction\":\"max\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [0, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 0, 2, [是, 是, 是], 是, 4], [2, 1, 0, [是, 是, 是], 是, 0], [3, 2, 2, [是, 是, 是], 是, 4]], 4, [1, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [0, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 0, 2, [是, 是, 是], 是, 4], [2, 1, 0, [是, 是, 是], 是, 0], [3, 2, 2, [是, 是, 是], 是, 4]], 4, [1, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216088,"parameters":{"points":[[0,0],[1,0],[2,2],[0,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,8]],"objective":[0,2],"direction":"max","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]],\"direction\":\"max\",\"objective\":[0,2],\"points\":[[0,0],[0,2],[1,0],[2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0089","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,1],[2,3],[1,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]],\"objective\":[1,2],\"direction\":\"min\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [1, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 1, [是, 是, 是], 是, 3], [2, 1, 2, [是, 是, 是], 是, 5], [3, 2, 3, [是, 是, 是], 是, 8]], 0, [0])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [1, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 1, [是, 是, 是], 是, 3], [2, 1, 2, [是, 是, 是], 是, 5], [3, 2, 3, [是, 是, 是], 是, 8]], 0, [0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216089,"parameters":{"points":[[0,0],[1,1],[2,3],[1,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,9]],"objective":[1,2],"direction":"min","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]],\"direction\":\"min\",\"objective\":[1,2],\"points\":[[0,0],[1,1],[1,2],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0090","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,2],[2,4],[2,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"objective\":[2,2],\"direction\":\"max\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [2, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 2, [是, 是, 是], 是, 6], [2, 2, 2, [是, 是, 否], 否, 8], [3, 2, 4, [是, 是, 否], 否, 12]], 6, [1])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [2, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 2, [是, 是, 是], 是, 6], [2, 2, 2, [是, 是, 否], 否, 8], [3, 2, 4, [是, 是, 否], 否, 12]], 6, [1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216090,"parameters":{"points":[[0,0],[1,2],[2,4],[2,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,3]],"objective":[2,2],"direction":"max","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"direction\":\"max\",\"objective\":[2,2],\"points\":[[0,0],[1,2],[2,2],[2,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0091","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,3],[2,0],[3,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"objective\":[-2,2],\"direction\":\"min\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [-2, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 3, [是, 是, 是], 是, 4], [2, 2, 0, [是, 是, 是], 是, -4], [3, 3, 2, [是, 是, 否], 否, -2]], -4, [2])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [-2, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 3, [是, 是, 是], 是, 4], [2, 2, 0, [是, 是, 是], 是, -4], [3, 3, 2, [是, 是, 否], 否, -2]], -4, [2])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216091,"parameters":{"points":[[0,0],[1,3],[2,0],[3,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,4]],"objective":[-2,2],"direction":"min","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"direction\":\"min\",\"objective\":[-2,2],\"points\":[[0,0],[1,3],[2,0],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0092","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,0],[2,1],[4,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"objective\":[-1,2],\"direction\":\"max\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [-1, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 0, [是, 是, 是], 是, -1], [2, 2, 1, [是, 是, 是], 是, 0], [3, 4, 2, [是, 是, 否], 否, 0]], 0, [0, 2])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [-1, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 0, [是, 是, 是], 是, -1], [2, 2, 1, [是, 是, 是], 是, 0], [3, 4, 2, [是, 是, 否], 否, 0]], 0, [0, 2])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216092,"parameters":{"points":[[0,0],[1,0],[2,1],[4,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,5]],"objective":[-1,2],"direction":"max","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"direction\":\"max\",\"objective\":[-1,2],\"points\":[[0,0],[1,0],[2,1],[4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0093","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,1],[2,2],[5,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"objective\":[0,2],\"direction\":\"min\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [0, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 1, [是, 是, 是], 是, 2], [2, 2, 2, [是, 是, 是], 是, 4], [3, 5, 2, [是, 是, 否], 否, 4]], 0, [0])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [0, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 1, [是, 是, 是], 是, 2], [2, 2, 2, [是, 是, 是], 是, 4], [3, 5, 2, [是, 是, 否], 否, 4]], 0, [0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216093,"parameters":{"points":[[0,0],[1,1],[2,2],[5,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,6]],"objective":[0,2],"direction":"min","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"direction\":\"min\",\"objective\":[0,2],\"points\":[[0,0],[1,1],[2,2],[5,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0094","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,2],[2,3],[0,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]],\"objective\":[1,2],\"direction\":\"max\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [1, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 0, 2, [是, 是, 是], 是, 4], [2, 1, 2, [是, 是, 是], 是, 5], [3, 2, 3, [是, 是, 是], 是, 8]], 8, [3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [1, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 0, 2, [是, 是, 是], 是, 4], [2, 1, 2, [是, 是, 是], 是, 5], [3, 2, 3, [是, 是, 是], 是, 8]], 8, [3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216094,"parameters":{"points":[[0,0],[1,2],[2,3],[0,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,7]],"objective":[1,2],"direction":"max","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,7]],\"direction\":\"max\",\"objective\":[1,2],\"points\":[[0,0],[0,2],[1,2],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0095","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,3],[2,4],[1,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]],\"objective\":[2,2],\"direction\":\"min\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [2, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 2, [是, 是, 是], 是, 6], [2, 1, 3, [是, 是, 是], 是, 8], [3, 2, 4, [是, 是, 是], 是, 12]], 0, [0])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [2, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 2, [是, 是, 是], 是, 6], [2, 1, 3, [是, 是, 是], 是, 8], [3, 2, 4, [是, 是, 是], 是, 12]], 0, [0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216095,"parameters":{"points":[[0,0],[1,3],[2,4],[1,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,8]],"objective":[2,2],"direction":"min","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,8]],\"direction\":\"min\",\"objective\":[2,2],\"points\":[[0,0],[1,2],[1,3],[2,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0096","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,0],[2,0],[2,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]],\"objective\":[-2,2],\"direction\":\"max\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [-2, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 0, [是, 是, 是], 是, -2], [2, 2, 0, [是, 是, 是], 是, -4], [3, 2, 2, [是, 是, 是], 是, 0]], 0, [0, 3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [-2, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 0, [是, 是, 是], 是, -2], [2, 2, 0, [是, 是, 是], 是, -4], [3, 2, 2, [是, 是, 是], 是, 0]], 0, [0, 3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216096,"parameters":{"points":[[0,0],[1,0],[2,0],[2,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,9]],"objective":[-2,2],"direction":"max","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,9]],\"direction\":\"max\",\"objective\":[-2,2],\"points\":[[0,0],[1,0],[2,0],[2,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0097","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,1],[2,1],[3,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"objective\":[-1,2],\"direction\":\"min\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [-1, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 1, [是, 是, 是], 是, 1], [2, 2, 1, [是, 是, 是], 是, 0], [3, 3, 2, [是, 是, 否], 否, 1]], 0, [0, 2])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [-1, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 1, [是, 是, 是], 是, 1], [2, 2, 1, [是, 是, 是], 是, 0], [3, 3, 2, [是, 是, 否], 否, 1]], 0, [0, 2])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216097,"parameters":{"points":[[0,0],[1,1],[2,1],[3,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,3]],"objective":[-1,2],"direction":"min","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,3]],\"direction\":\"min\",\"objective\":[-1,2],\"points\":[[0,0],[1,1],[2,1],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0098","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,2],[2,2],[4,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"objective\":[0,2],\"direction\":\"max\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [0, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 2, [是, 是, 是], 是, 4], [2, 2, 2, [是, 是, 是], 是, 4], [3, 4, 2, [是, 是, 否], 否, 4]], 4, [1, 2])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [0, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 2, [是, 是, 是], 是, 4], [2, 2, 2, [是, 是, 是], 是, 4], [3, 4, 2, [是, 是, 否], 否, 4]], 4, [1, 2])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216098,"parameters":{"points":[[0,0],[1,2],[2,2],[4,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,4]],"objective":[0,2],"direction":"max","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,4]],\"direction\":\"max\",\"objective\":[0,2],\"points\":[[0,0],[1,2],[2,2],[4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0099","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,3],[2,3],[5,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"objective\":[1,2],\"direction\":\"min\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [1, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 3, [是, 是, 是], 是, 7], [2, 2, 3, [是, 是, 是], 是, 8], [3, 5, 2, [是, 是, 否], 否, 9]], 0, [0])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [1, 2], min, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 1, 3, [是, 是, 是], 是, 7], [2, 2, 3, [是, 是, 是], 是, 8], [3, 5, 2, [是, 是, 否], 否, 9]], 0, [0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216099,"parameters":{"points":[[0,0],[1,3],[2,3],[5,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,5]],"objective":[1,2],"direction":"min","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,5]],\"direction\":\"min\",\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,3],[5,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r06-linear-programming-0100","batch_id":"batch-20261013-advance-20261021-r06-linear-programming-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-programming"],"title_zh":"有限線性規劃候選","stem_zh":"完整明示有限候選網格。操作=lp-finite-optimum；資料={\"points\":[[0,0],[1,0],[2,4],[0,2]],\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"objective\":[2,2],\"direction\":\"max\"}。請依 [constraints,objective,direction,point_rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [2, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 0, 2, [是, 是, 是], 是, 4], [2, 1, 0, [是, 是, 是], 是, 2], [3, 2, 4, [是, 是, 是], 是, 12]], 12, [3])","explanation_zh":"應用擴展核對=([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [2, 2], max, [[0, 0, 0, [是, 是, 是], 是, 0], [1, 0, 2, [是, 是, 是], 是, 4], [2, 1, 0, [是, 是, 是], 是, 2], [3, 2, 4, [是, 是, 是], 是, 12]], 12, [3])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；只稱所給候選中最佳；不宣稱一般LP全域最優。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限線性規劃候選"]},"variant":{"family_id":"qf-app21-lp-finite-optimum","seed":202610216100,"parameters":{"points":[[0,0],[1,0],[2,4],[0,2]],"constraints":[[-1,0,0],[0,-1,0],[1,1,6]],"objective":[2,2],"direction":"max","domain":"Finite_linear_program_candidate_grid","operation":"lp-finite-optimum","semantic_template":"qf-app21-lp-finite-optimum/{\"constraints\":[[-1,0,0],[0,-1,0],[1,1,6]],\"direction\":\"max\",\"objective\":[2,2],\"points\":[[0,0],[0,2],[1,0],[2,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}