# 線性規劃標準形基礎 · 脈衝 R06

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations · 2026-10-15 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

[欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[1,1],[-1,2]],"b":[4,2],"c":[3,-1]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[1, 1], [-1, 2]], [4, 2], [3, -1], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[1, 1], [-1, 2]], [4, 2], [3, -1], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0001/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 2. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[2,1],[-1,3]],"b":[6,3],"c":[4,-2]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[2, 1], [-1, 3]], [6, 3], [4, -2], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[2, 1], [-1, 3]], [6, 3], [4, -2], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0002/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 3. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[3,1],[-1,4]],"b":[8,4],"c":[5,-3]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[3, 1], [-1, 4]], [8, 4], [5, -3], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[3, 1], [-1, 4]], [8, 4], [5, -3], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0003/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 4. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[4,1],[-1,5]],"b":[10,5],"c":[6,-4]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[4, 1], [-1, 5]], [10, 5], [6, -4], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[4, 1], [-1, 5]], [10, 5], [6, -4], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0004/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 5. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[5,1],[-1,6]],"b":[12,6],"c":[7,-5]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[5, 1], [-1, 6]], [12, 6], [7, -5], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[5, 1], [-1, 6]], [12, 6], [7, -5], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0005/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 6. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[6,1],[-1,7]],"b":[14,7],"c":[8,-6]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[6, 1], [-1, 7]], [14, 7], [8, -6], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[6, 1], [-1, 7]], [14, 7], [8, -6], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0006/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 7. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[7,1],[-1,8]],"b":[16,8],"c":[9,-7]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[7, 1], [-1, 8]], [16, 8], [9, -7], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[7, 1], [-1, 8]], [16, 8], [9, -7], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0007/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 8. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[8,1],[-1,9]],"b":[18,9],"c":[10,-8]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[8, 1], [-1, 9]], [18, 9], [10, -8], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[8, 1], [-1, 9]], [18, 9], [10, -8], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0008/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 9. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[9,1],[-1,10]],"b":[20,10],"c":[11,-9]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[9, 1], [-1, 10]], [20, 10], [11, -9], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[9, 1], [-1, 10]], [20, 10], [11, -9], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0009/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 10. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[10,1],[-1,11]],"b":[22,11],"c":[12,-10]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[10, 1], [-1, 11]], [22, 11], [12, -10], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[10, 1], [-1, 11]], [22, 11], [12, -10], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0010/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 11. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[11,1],[-1,12]],"b":[24,12],"c":[13,-11]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[11, 1], [-1, 12]], [24, 12], [13, -11], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[11, 1], [-1, 12]], [24, 12], [13, -11], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0011/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 12. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[12,1],[-1,13]],"b":[26,13],"c":[14,-12]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[12, 1], [-1, 13]], [26, 13], [14, -12], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[12, 1], [-1, 13]], [26, 13], [14, -12], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0012/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 13. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[13,1],[-1,14]],"b":[28,14],"c":[15,-13]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[13, 1], [-1, 14]], [28, 14], [15, -13], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[13, 1], [-1, 14]], [28, 14], [15, -13], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0013/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 14. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[14,1],[-1,15]],"b":[30,15],"c":[16,-14]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[14, 1], [-1, 15]], [30, 15], [16, -14], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[14, 1], [-1, 15]], [30, 15], [16, -14], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0014/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 15. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[15,1],[-1,16]],"b":[32,16],"c":[17,-15]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[15, 1], [-1, 16]], [32, 16], [17, -15], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[15, 1], [-1, 16]], [32, 16], [17, -15], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0015/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 16. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[16,1],[-1,17]],"b":[34,17],"c":[18,-16]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[16, 1], [-1, 17]], [34, 17], [18, -16], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[16, 1], [-1, 17]], [34, 17], [18, -16], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0016/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 17. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[17,1],[-1,18]],"b":[36,18],"c":[19,-17]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[17, 1], [-1, 18]], [36, 18], [19, -17], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[17, 1], [-1, 18]], [36, 18], [19, -17], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0017/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 18. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[18,1],[-1,19]],"b":[38,19],"c":[20,-18]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[18, 1], [-1, 19]], [38, 19], [20, -18], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[18, 1], [-1, 19]], [38, 19], [20, -18], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0018/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 19. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[19,1],[-1,20]],"b":[40,20],"c":[21,-19]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[19, 1], [-1, 20]], [40, 20], [21, -19], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[19, 1], [-1, 20]], [40, 20], [21, -19], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0019/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 20. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[20,1],[-1,21]],"b":[42,21],"c":[22,-20]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[20, 1], [-1, 21]], [42, 21], [22, -20], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[20, 1], [-1, 21]], [42, 21], [22, -20], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0020/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 21. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[21,1],[-1,22]],"b":[44,22],"c":[23,-21]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[21, 1], [-1, 22]], [44, 22], [23, -21], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[21, 1], [-1, 22]], [44, 22], [23, -21], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0021/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 22. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[22,1],[-1,23]],"b":[46,23],"c":[24,-22]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[22, 1], [-1, 23]], [46, 23], [24, -22], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[22, 1], [-1, 23]], [46, 23], [24, -22], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0022/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 23. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[23,1],[-1,24]],"b":[48,24],"c":[25,-23]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[23, 1], [-1, 24]], [48, 24], [25, -23], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[23, 1], [-1, 24]], [48, 24], [25, -23], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0023/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 24. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[24,1],[-1,25]],"b":[50,25],"c":[26,-24]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[24, 1], [-1, 25]], [50, 25], [26, -24], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[24, 1], [-1, 25]], [50, 25], [26, -24], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0024/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 25. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-dimension-sign-qualification；資料={"A":[[25,1],[-1,26]],"b":[52,26],"c":[27,-25]}。請依 [constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate] 欄序回答。

查看答案與解釋(2, 2, [[25, 1], [-1, 26]], [52, 26], [27, -25], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)

Wave6第八層核對=(2, 2, [[25, 1], [-1, 26]], [52, 26], [27, -25], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, 是, one_fixed_standard_form_convention)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0025/)

線性規劃標準形 · qf-mod45-lp-standard-dimension-sign-qualification · candidate





## 26. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[1,1],[1,1]],"b":[4,4],"c":[2,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [2, 2], [4, 4], [2, 2], 是, 是, 是, 是, 是, 3, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [2, 2], [4, 4], [2, 2], 是, 是, 是, 是, 是, 3, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0026/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 27. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[2,1],[1,2]],"b":[5,5],"c":[3,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [3, 3], [5, 5], [2, 2], 是, 是, 是, 是, 是, 4, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [3, 3], [5, 5], [2, 2], 是, 是, 是, 是, 是, 4, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0027/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 28. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[3,1],[1,3]],"b":[6,6],"c":[4,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [4, 4], [6, 6], [2, 2], 是, 是, 是, 是, 是, 5, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [4, 4], [6, 6], [2, 2], 是, 是, 是, 是, 是, 5, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0028/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 29. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[4,1],[1,4]],"b":[7,7],"c":[5,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [5, 5], [7, 7], [2, 2], 是, 是, 是, 是, 是, 6, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [5, 5], [7, 7], [2, 2], 是, 是, 是, 是, 是, 6, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0029/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 30. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[5,1],[1,5]],"b":[8,8],"c":[6,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [6, 6], [8, 8], [2, 2], 是, 是, 是, 是, 是, 7, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [6, 6], [8, 8], [2, 2], 是, 是, 是, 是, 是, 7, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0030/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 31. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[6,1],[1,6]],"b":[9,9],"c":[7,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [7, 7], [9, 9], [2, 2], 是, 是, 是, 是, 是, 8, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [7, 7], [9, 9], [2, 2], 是, 是, 是, 是, 是, 8, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0031/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 32. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[7,1],[1,7]],"b":[10,10],"c":[8,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [8, 8], [10, 10], [2, 2], 是, 是, 是, 是, 是, 9, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [8, 8], [10, 10], [2, 2], 是, 是, 是, 是, 是, 9, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0032/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 33. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[8,1],[1,8]],"b":[11,11],"c":[9,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [9, 9], [11, 11], [2, 2], 是, 是, 是, 是, 是, 10, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [9, 9], [11, 11], [2, 2], 是, 是, 是, 是, 是, 10, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0033/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 34. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[9,1],[1,9]],"b":[12,12],"c":[10,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [10, 10], [12, 12], [2, 2], 是, 是, 是, 是, 是, 11, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [10, 10], [12, 12], [2, 2], 是, 是, 是, 是, 是, 11, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0034/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 35. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[10,1],[1,10]],"b":[13,13],"c":[11,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [11, 11], [13, 13], [2, 2], 是, 是, 是, 是, 是, 12, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [11, 11], [13, 13], [2, 2], 是, 是, 是, 是, 是, 12, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0035/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 36. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[11,1],[1,11]],"b":[14,14],"c":[12,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [12, 12], [14, 14], [2, 2], 是, 是, 是, 是, 是, 13, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [12, 12], [14, 14], [2, 2], 是, 是, 是, 是, 是, 13, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0036/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 37. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[12,1],[1,12]],"b":[15,15],"c":[13,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [13, 13], [15, 15], [2, 2], 是, 是, 是, 是, 是, 14, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [13, 13], [15, 15], [2, 2], 是, 是, 是, 是, 是, 14, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0037/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 38. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[13,1],[1,13]],"b":[16,16],"c":[14,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [14, 14], [16, 16], [2, 2], 是, 是, 是, 是, 是, 15, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [14, 14], [16, 16], [2, 2], 是, 是, 是, 是, 是, 15, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0038/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 39. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[14,1],[1,14]],"b":[17,17],"c":[15,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [15, 15], [17, 17], [2, 2], 是, 是, 是, 是, 是, 16, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [15, 15], [17, 17], [2, 2], 是, 是, 是, 是, 是, 16, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0039/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 40. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[15,1],[1,15]],"b":[18,18],"c":[16,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [16, 16], [18, 18], [2, 2], 是, 是, 是, 是, 是, 17, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [16, 16], [18, 18], [2, 2], 是, 是, 是, 是, 是, 17, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0040/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 41. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[16,1],[1,16]],"b":[19,19],"c":[17,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [17, 17], [19, 19], [2, 2], 是, 是, 是, 是, 是, 18, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [17, 17], [19, 19], [2, 2], 是, 是, 是, 是, 是, 18, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0041/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 42. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[17,1],[1,17]],"b":[20,20],"c":[18,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [18, 18], [20, 20], [2, 2], 是, 是, 是, 是, 是, 19, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [18, 18], [20, 20], [2, 2], 是, 是, 是, 是, 是, 19, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0042/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 43. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[18,1],[1,18]],"b":[21,21],"c":[19,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [19, 19], [21, 21], [2, 2], 是, 是, 是, 是, 是, 20, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [19, 19], [21, 21], [2, 2], 是, 是, 是, 是, 是, 20, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0043/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 44. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[19,1],[1,19]],"b":[22,22],"c":[20,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [20, 20], [22, 22], [2, 2], 是, 是, 是, 是, 是, 21, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [20, 20], [22, 22], [2, 2], 是, 是, 是, 是, 是, 21, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0044/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 45. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[20,1],[1,20]],"b":[23,23],"c":[21,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [21, 21], [23, 23], [2, 2], 是, 是, 是, 是, 是, 22, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [21, 21], [23, 23], [2, 2], 是, 是, 是, 是, 是, 22, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0045/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 46. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[21,1],[1,21]],"b":[24,24],"c":[22,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [22, 22], [24, 24], [2, 2], 是, 是, 是, 是, 是, 23, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [22, 22], [24, 24], [2, 2], 是, 是, 是, 是, 是, 23, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0046/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 47. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[22,1],[1,22]],"b":[25,25],"c":[23,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [23, 23], [25, 25], [2, 2], 是, 是, 是, 是, 是, 24, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [23, 23], [25, 25], [2, 2], 是, 是, 是, 是, 是, 24, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0047/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 48. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[23,1],[1,23]],"b":[26,26],"c":[24,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [24, 24], [26, 26], [2, 2], 是, 是, 是, 是, 是, 25, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [24, 24], [26, 26], [2, 2], 是, 是, 是, 是, 是, 25, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0048/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 49. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[24,1],[1,24]],"b":[27,27],"c":[25,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [25, 25], [27, 27], [2, 2], 是, 是, 是, 是, 是, 26, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [25, 25], [27, 27], [2, 2], 是, 是, 是, 是, 是, 26, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0049/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 50. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-slack-conversion；資料={"A":[[25,1],[1,25]],"b":[28,28],"c":[26,1],"x":[1,1]}。請依 [x, Ax, b, slack, x_nonnegative, inequalities_hold, slack_nonnegative, feasible, feasibility_equivalence_holds, objective_value, certificate] 欄序回答。

查看答案與解釋([1, 1], [26, 26], [28, 28], [2, 2], 是, 是, 是, 是, 是, 27, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)

Wave6第八層核對=([1, 1], [26, 26], [28, 28], [2, 2], 是, 是, 是, 是, 是, 27, x_maps_to_(x,b-Ax)_and_every_nonnegative_slack_equality_point_maps_back_bijectively)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0050/)

線性規劃標準形 · qf-mod45-lp-standard-slack-conversion · candidate





## 51. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[1,-2,3],"objective_coefficient":4,"value":1}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([1, -2, 3], 4, 1, 1, 0, 1, [1, -2, 3], [1, -2, 3], 是, 4, 4, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([1, -2, 3], 4, 1, 1, 0, 1, [1, -2, 3], [1, -2, 3], 是, 4, 4, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0051/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 52. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[2,-3,4],"objective_coefficient":5,"value":-2}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([2, -3, 4], 5, -2, 0, 2, -2, [-4, 6, -8], [-4, 6, -8], 是, -10, -10, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([2, -3, 4], 5, -2, 0, 2, -2, [-4, 6, -8], [-4, 6, -8], 是, -10, -10, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0052/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 53. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[3,-4,5],"objective_coefficient":6,"value":3}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([3, -4, 5], 6, 3, 3, 0, 3, [9, -12, 15], [9, -12, 15], 是, 18, 18, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([3, -4, 5], 6, 3, 3, 0, 3, [9, -12, 15], [9, -12, 15], 是, 18, 18, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0053/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 54. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[4,-5,6],"objective_coefficient":7,"value":-4}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([4, -5, 6], 7, -4, 0, 4, -4, [-16, 20, -24], [-16, 20, -24], 是, -28, -28, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([4, -5, 6], 7, -4, 0, 4, -4, [-16, 20, -24], [-16, 20, -24], 是, -28, -28, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0054/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 55. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[5,-6,7],"objective_coefficient":8,"value":5}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([5, -6, 7], 8, 5, 5, 0, 5, [25, -30, 35], [25, -30, 35], 是, 40, 40, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([5, -6, 7], 8, 5, 5, 0, 5, [25, -30, 35], [25, -30, 35], 是, 40, 40, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0055/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 56. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[6,-7,8],"objective_coefficient":9,"value":-6}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([6, -7, 8], 9, -6, 0, 6, -6, [-36, 42, -48], [-36, 42, -48], 是, -54, -54, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([6, -7, 8], 9, -6, 0, 6, -6, [-36, 42, -48], [-36, 42, -48], 是, -54, -54, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0056/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 57. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[7,-8,9],"objective_coefficient":10,"value":7}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([7, -8, 9], 10, 7, 7, 0, 7, [49, -56, 63], [49, -56, 63], 是, 70, 70, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([7, -8, 9], 10, 7, 7, 0, 7, [49, -56, 63], [49, -56, 63], 是, 70, 70, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0057/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 58. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[8,-9,10],"objective_coefficient":11,"value":-8}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([8, -9, 10], 11, -8, 0, 8, -8, [-64, 72, -80], [-64, 72, -80], 是, -88, -88, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([8, -9, 10], 11, -8, 0, 8, -8, [-64, 72, -80], [-64, 72, -80], 是, -88, -88, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0058/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 59. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[9,-10,11],"objective_coefficient":12,"value":9}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([9, -10, 11], 12, 9, 9, 0, 9, [81, -90, 99], [81, -90, 99], 是, 108, 108, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([9, -10, 11], 12, 9, 9, 0, 9, [81, -90, 99], [81, -90, 99], 是, 108, 108, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0059/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 60. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[10,-11,12],"objective_coefficient":13,"value":-10}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([10, -11, 12], 13, -10, 0, 10, -10, [-100, 110, -120], [-100, 110, -120], 是, -130, -130, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([10, -11, 12], 13, -10, 0, 10, -10, [-100, 110, -120], [-100, 110, -120], 是, -130, -130, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0060/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 61. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[11,-12,13],"objective_coefficient":14,"value":11}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([11, -12, 13], 14, 11, 11, 0, 11, [121, -132, 143], [121, -132, 143], 是, 154, 154, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([11, -12, 13], 14, 11, 11, 0, 11, [121, -132, 143], [121, -132, 143], 是, 154, 154, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0061/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 62. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[12,-13,14],"objective_coefficient":15,"value":-12}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([12, -13, 14], 15, -12, 0, 12, -12, [-144, 156, -168], [-144, 156, -168], 是, -180, -180, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([12, -13, 14], 15, -12, 0, 12, -12, [-144, 156, -168], [-144, 156, -168], 是, -180, -180, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0062/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 63. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[13,-14,15],"objective_coefficient":16,"value":13}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([13, -14, 15], 16, 13, 13, 0, 13, [169, -182, 195], [169, -182, 195], 是, 208, 208, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([13, -14, 15], 16, 13, 13, 0, 13, [169, -182, 195], [169, -182, 195], 是, 208, 208, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0063/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 64. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[14,-15,16],"objective_coefficient":17,"value":-14}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([14, -15, 16], 17, -14, 0, 14, -14, [-196, 210, -224], [-196, 210, -224], 是, -238, -238, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([14, -15, 16], 17, -14, 0, 14, -14, [-196, 210, -224], [-196, 210, -224], 是, -238, -238, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0064/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 65. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[15,-16,17],"objective_coefficient":18,"value":15}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([15, -16, 17], 18, 15, 15, 0, 15, [225, -240, 255], [225, -240, 255], 是, 270, 270, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([15, -16, 17], 18, 15, 15, 0, 15, [225, -240, 255], [225, -240, 255], 是, 270, 270, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0065/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 66. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[16,-17,18],"objective_coefficient":19,"value":-16}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([16, -17, 18], 19, -16, 0, 16, -16, [-256, 272, -288], [-256, 272, -288], 是, -304, -304, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([16, -17, 18], 19, -16, 0, 16, -16, [-256, 272, -288], [-256, 272, -288], 是, -304, -304, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0066/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 67. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[17,-18,19],"objective_coefficient":20,"value":17}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([17, -18, 19], 20, 17, 17, 0, 17, [289, -306, 323], [289, -306, 323], 是, 340, 340, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([17, -18, 19], 20, 17, 17, 0, 17, [289, -306, 323], [289, -306, 323], 是, 340, 340, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0067/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 68. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[18,-19,20],"objective_coefficient":21,"value":-18}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([18, -19, 20], 21, -18, 0, 18, -18, [-324, 342, -360], [-324, 342, -360], 是, -378, -378, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([18, -19, 20], 21, -18, 0, 18, -18, [-324, 342, -360], [-324, 342, -360], 是, -378, -378, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0068/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 69. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[19,-20,21],"objective_coefficient":22,"value":19}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([19, -20, 21], 22, 19, 19, 0, 19, [361, -380, 399], [361, -380, 399], 是, 418, 418, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([19, -20, 21], 22, 19, 19, 0, 19, [361, -380, 399], [361, -380, 399], 是, 418, 418, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0069/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 70. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[20,-21,22],"objective_coefficient":23,"value":-20}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([20, -21, 22], 23, -20, 0, 20, -20, [-400, 420, -440], [-400, 420, -440], 是, -460, -460, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([20, -21, 22], 23, -20, 0, 20, -20, [-400, 420, -440], [-400, 420, -440], 是, -460, -460, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0070/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 71. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[21,-22,23],"objective_coefficient":24,"value":21}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([21, -22, 23], 24, 21, 21, 0, 21, [441, -462, 483], [441, -462, 483], 是, 504, 504, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([21, -22, 23], 24, 21, 21, 0, 21, [441, -462, 483], [441, -462, 483], 是, 504, 504, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0071/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 72. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[22,-23,24],"objective_coefficient":25,"value":-22}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([22, -23, 24], 25, -22, 0, 22, -22, [-484, 506, -528], [-484, 506, -528], 是, -550, -550, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([22, -23, 24], 25, -22, 0, 22, -22, [-484, 506, -528], [-484, 506, -528], 是, -550, -550, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0072/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 73. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[23,-24,25],"objective_coefficient":26,"value":23}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([23, -24, 25], 26, 23, 23, 0, 23, [529, -552, 575], [529, -552, 575], 是, 598, 598, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([23, -24, 25], 26, 23, 23, 0, 23, [529, -552, 575], [529, -552, 575], 是, 598, 598, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0073/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 74. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[24,-25,26],"objective_coefficient":27,"value":-24}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([24, -25, 26], 27, -24, 0, 24, -24, [-576, 600, -624], [-576, 600, -624], 是, -648, -648, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([24, -25, 26], 27, -24, 0, 24, -24, [-576, 600, -624], [-576, 600, -624], 是, -648, -648, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0074/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 75. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-unrestricted-split；資料={"column":[25,-26,27],"objective_coefficient":28,"value":25}。請依 [column, objective_coefficient, value, x_plus, x_minus, reconstructed_value, original_column_contribution, split_column_contribution, columns_equal, original_objective_contribution, split_objective_contribution, objectives_equal, certificate] 欄序回答。

此處給一組canonical非負split；其他兩分量同加非負數也可表示同一value，所以split不是全體表示間的一一對應。

查看答案與解釋([25, -26, 27], 28, 25, 25, 0, 25, [625, -650, 675], [625, -650, 675], 是, 700, 700, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)

Wave6第八層核對=([25, -26, 27], 28, 25, 25, 0, 25, [625, -650, 675], [625, -650, 675], 是, 700, 700, 是, x=x_plus-x_minus_with_both_nonnegative_preserves_column_and_objective_contribution)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0075/)

線性規劃標準形 · qf-mod45-lp-standard-unrestricted-split · candidate





## 76. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"greater_equal","coefficients":[1,-2,1],"rhs":3}。請依 [mode, coefficients, rhs, negated_coefficients, negated_rhs, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(greater_equal, [1, -2, 1], 3, [-1, 2, -1], -3, multiply_constraint_by_minus_one_to_obtain_less_equal)

Wave6第八層核對=(greater_equal, [1, -2, 1], 3, [-1, 2, -1], -3, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0076/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 77. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"equality","coefficients":[2,-3,1],"rhs":4}。請依 [mode, coefficients, rhs, less_equal_row, opposite_less_equal_row, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(equality, [2, -3, 1], 4, [[2, -3, 1], 4], [[-2, 3, -1], -4], replace_equality_by_two_opposite_less_equal_constraints)

Wave6第八層核對=(equality, [2, -3, 1], 4, [[2, -3, 1], 4], [[-2, 3, -1], -4], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0077/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 78. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"minimize","coefficients":[3,-4,1],"rhs":0}。請依 [mode, objective_coefficients, maximization_coefficients, conversion_rule, optimality_certificate, boundary] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(minimize, [3, -4, 1], [-3, 4, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)

Wave6第八層核對=(minimize, [3, -4, 1], [-3, 4, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0078/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 79. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"greater_equal","coefficients":[4,-5,1],"rhs":6}。請依 [mode, coefficients, rhs, negated_coefficients, negated_rhs, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(greater_equal, [4, -5, 1], 6, [-4, 5, -1], -6, multiply_constraint_by_minus_one_to_obtain_less_equal)

Wave6第八層核對=(greater_equal, [4, -5, 1], 6, [-4, 5, -1], -6, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0079/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 80. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"equality","coefficients":[5,-6,1],"rhs":7}。請依 [mode, coefficients, rhs, less_equal_row, opposite_less_equal_row, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(equality, [5, -6, 1], 7, [[5, -6, 1], 7], [[-5, 6, -1], -7], replace_equality_by_two_opposite_less_equal_constraints)

Wave6第八層核對=(equality, [5, -6, 1], 7, [[5, -6, 1], 7], [[-5, 6, -1], -7], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0080/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 81. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"minimize","coefficients":[6,-7,1],"rhs":0}。請依 [mode, objective_coefficients, maximization_coefficients, conversion_rule, optimality_certificate, boundary] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(minimize, [6, -7, 1], [-6, 7, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)

Wave6第八層核對=(minimize, [6, -7, 1], [-6, 7, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0081/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 82. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"greater_equal","coefficients":[7,-8,1],"rhs":9}。請依 [mode, coefficients, rhs, negated_coefficients, negated_rhs, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(greater_equal, [7, -8, 1], 9, [-7, 8, -1], -9, multiply_constraint_by_minus_one_to_obtain_less_equal)

Wave6第八層核對=(greater_equal, [7, -8, 1], 9, [-7, 8, -1], -9, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0082/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 83. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"equality","coefficients":[8,-9,1],"rhs":10}。請依 [mode, coefficients, rhs, less_equal_row, opposite_less_equal_row, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(equality, [8, -9, 1], 10, [[8, -9, 1], 10], [[-8, 9, -1], -10], replace_equality_by_two_opposite_less_equal_constraints)

Wave6第八層核對=(equality, [8, -9, 1], 10, [[8, -9, 1], 10], [[-8, 9, -1], -10], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0083/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 84. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"minimize","coefficients":[9,-10,1],"rhs":0}。請依 [mode, objective_coefficients, maximization_coefficients, conversion_rule, optimality_certificate, boundary] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(minimize, [9, -10, 1], [-9, 10, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)

Wave6第八層核對=(minimize, [9, -10, 1], [-9, 10, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0084/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 85. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"greater_equal","coefficients":[10,-11,1],"rhs":12}。請依 [mode, coefficients, rhs, negated_coefficients, negated_rhs, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(greater_equal, [10, -11, 1], 12, [-10, 11, -1], -12, multiply_constraint_by_minus_one_to_obtain_less_equal)

Wave6第八層核對=(greater_equal, [10, -11, 1], 12, [-10, 11, -1], -12, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0085/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 86. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"equality","coefficients":[11,-12,1],"rhs":13}。請依 [mode, coefficients, rhs, less_equal_row, opposite_less_equal_row, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(equality, [11, -12, 1], 13, [[11, -12, 1], 13], [[-11, 12, -1], -13], replace_equality_by_two_opposite_less_equal_constraints)

Wave6第八層核對=(equality, [11, -12, 1], 13, [[11, -12, 1], 13], [[-11, 12, -1], -13], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0086/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 87. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"minimize","coefficients":[12,-13,1],"rhs":0}。請依 [mode, objective_coefficients, maximization_coefficients, conversion_rule, optimality_certificate, boundary] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(minimize, [12, -13, 1], [-12, 13, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)

Wave6第八層核對=(minimize, [12, -13, 1], [-12, 13, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0087/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 88. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"greater_equal","coefficients":[13,-14,1],"rhs":15}。請依 [mode, coefficients, rhs, negated_coefficients, negated_rhs, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(greater_equal, [13, -14, 1], 15, [-13, 14, -1], -15, multiply_constraint_by_minus_one_to_obtain_less_equal)

Wave6第八層核對=(greater_equal, [13, -14, 1], 15, [-13, 14, -1], -15, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0088/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 89. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"equality","coefficients":[14,-15,1],"rhs":16}。請依 [mode, coefficients, rhs, less_equal_row, opposite_less_equal_row, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(equality, [14, -15, 1], 16, [[14, -15, 1], 16], [[-14, 15, -1], -16], replace_equality_by_two_opposite_less_equal_constraints)

Wave6第八層核對=(equality, [14, -15, 1], 16, [[14, -15, 1], 16], [[-14, 15, -1], -16], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0089/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 90. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"minimize","coefficients":[15,-16,1],"rhs":0}。請依 [mode, objective_coefficients, maximization_coefficients, conversion_rule, optimality_certificate, boundary] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(minimize, [15, -16, 1], [-15, 16, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)

Wave6第八層核對=(minimize, [15, -16, 1], [-15, 16, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0090/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 91. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"greater_equal","coefficients":[16,-17,1],"rhs":18}。請依 [mode, coefficients, rhs, negated_coefficients, negated_rhs, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(greater_equal, [16, -17, 1], 18, [-16, 17, -1], -18, multiply_constraint_by_minus_one_to_obtain_less_equal)

Wave6第八層核對=(greater_equal, [16, -17, 1], 18, [-16, 17, -1], -18, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0091/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 92. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"equality","coefficients":[17,-18,1],"rhs":19}。請依 [mode, coefficients, rhs, less_equal_row, opposite_less_equal_row, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(equality, [17, -18, 1], 19, [[17, -18, 1], 19], [[-17, 18, -1], -19], replace_equality_by_two_opposite_less_equal_constraints)

Wave6第八層核對=(equality, [17, -18, 1], 19, [[17, -18, 1], 19], [[-17, 18, -1], -19], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0092/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 93. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"minimize","coefficients":[18,-19,1],"rhs":0}。請依 [mode, objective_coefficients, maximization_coefficients, conversion_rule, optimality_certificate, boundary] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(minimize, [18, -19, 1], [-18, 19, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)

Wave6第八層核對=(minimize, [18, -19, 1], [-18, 19, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0093/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 94. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"greater_equal","coefficients":[19,-20,1],"rhs":21}。請依 [mode, coefficients, rhs, negated_coefficients, negated_rhs, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(greater_equal, [19, -20, 1], 21, [-19, 20, -1], -21, multiply_constraint_by_minus_one_to_obtain_less_equal)

Wave6第八層核對=(greater_equal, [19, -20, 1], 21, [-19, 20, -1], -21, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0094/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 95. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"equality","coefficients":[20,-21,1],"rhs":22}。請依 [mode, coefficients, rhs, less_equal_row, opposite_less_equal_row, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(equality, [20, -21, 1], 22, [[20, -21, 1], 22], [[-20, 21, -1], -22], replace_equality_by_two_opposite_less_equal_constraints)

Wave6第八層核對=(equality, [20, -21, 1], 22, [[20, -21, 1], 22], [[-20, 21, -1], -22], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0095/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 96. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"minimize","coefficients":[21,-22,1],"rhs":0}。請依 [mode, objective_coefficients, maximization_coefficients, conversion_rule, optimality_certificate, boundary] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(minimize, [21, -22, 1], [-21, 22, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)

Wave6第八層核對=(minimize, [21, -22, 1], [-21, 22, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0096/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 97. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"greater_equal","coefficients":[22,-23,1],"rhs":24}。請依 [mode, coefficients, rhs, negated_coefficients, negated_rhs, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(greater_equal, [22, -23, 1], 24, [-22, 23, -1], -24, multiply_constraint_by_minus_one_to_obtain_less_equal)

Wave6第八層核對=(greater_equal, [22, -23, 1], 24, [-22, 23, -1], -24, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0097/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 98. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"equality","coefficients":[23,-24,1],"rhs":25}。請依 [mode, coefficients, rhs, less_equal_row, opposite_less_equal_row, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(equality, [23, -24, 1], 25, [[23, -24, 1], 25], [[-23, 24, -1], -25], replace_equality_by_two_opposite_less_equal_constraints)

Wave6第八層核對=(equality, [23, -24, 1], 25, [[23, -24, 1], 25], [[-23, 24, -1], -25], replace_equality_by_two_opposite_less_equal_constraints)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0098/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 99. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"minimize","coefficients":[24,-25,1],"rhs":0}。請依 [mode, objective_coefficients, maximization_coefficients, conversion_rule, optimality_certificate, boundary] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(minimize, [24, -25, 1], [-24, 25, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)

Wave6第八層核對=(minimize, [24, -25, 1], [-24, 25, -1], negate_objective_to_convert_minimize_to_maximize, 否, conversion_does_not_prove_feasible_bounded_or_optimal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0099/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate





## 100. 線性規劃標準形

固定maximize cTx、Ax≤b、x≥0的唯一standard-form convention。操作=lp-standard-convention-boundary；資料={"mode":"greater_equal","coefficients":[25,-26,1],"rhs":27}。請依 [mode, coefficients, rhs, negated_coefficients, negated_rhs, certificate] 欄序回答。

三種mode都有6欄但欄位角色不同，須依mode選取；minimize的rhs=0僅是來源sentinel，不是新增constraint。轉換不證可行、有界或最優。

查看答案與解釋(greater_equal, [25, -26, 1], 27, [-25, 26, -1], -27, multiply_constraint_by_minus_one_to_obtain_less_equal)

Wave6第八層核對=(greater_equal, [25, -26, 1], 27, [-25, 26, -1], -27, multiply_constraint_by_minus_one_to_obtain_less_equal)；依完整明示資料獨立重算；dimensions/sign先資格核對；slack與unrestricted split給雙向point representation；≥、equality與minimize轉換不證feasible、bounded、optimal或dual，且不得混用另一convention。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0100/)

線性規劃標準形 · qf-mod45-lp-standard-convention-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261114-r06-linear-program-standard-form-foundations/validation-report.json)