{"schema_version":"ocme-site-results-v1","locale":"zh-Hant","page_type":"derivations","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{"q":"mko-linear-programming"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-linear-programming-01","title":{"zh-Hant":"線性規劃：在明示候選中求最佳，並說明它不是連續最優","en":"Linear programming: the best supplied candidate, and why it is not the continuous optimum"},"summary":{"zh-Hant":"限制 3x+2y≤12、x+2y≤6、−x≤0、−y≤0，目標為最大化 L(x,y)=x+y。對明示的七個候選 P1=(0,0)、P2=(4,0)、P3=(3,1)、P4=(2,2)、P5=(0,3)、P6=(4,1)、P7=(3,2)，逐限制核對可行性，只在可行候選間比較目標值，求出候選中的最大值與全部最佳點；再以可行點 Q=(3,3/2) 與一個不等式證書證明連續可行域上的最大值是 9/2，而不是候選中的 4。","en":"Constraints 3x+2y≤12, x+2y≤6, −x≤0, −y≤0; objective: maximize L(x,y)=x+y. For the seven supplied candidates P1=(0,0), P2=(4,0), P3=(3,1), P4=(2,2), P5=(0,3), P6=(4,1), P7=(3,2), check feasibility constraint by constraint, compare objective values only among feasible candidates, and find the best value among the candidates and all points attaining it; then use the feasible point Q=(3,3/2) and an inequality certificate to prove that the maximum over the continuous feasible region is 9/2, not the candidate value 4."},"mko_ids":["mko-linear-programming"]}],"title":"概念推導導讀"}