# OCME ยท Knowledge & practice explorer 302 MKO / 1,441 families / 360 batches / 36,000 questions. 36,000 second-context math/bilingual reviewed; 0 display/symbol-checked candidates. Source questions: candidate. English: ai_candidate. No new proof, Lean, SREG or training. 25 results; page 1/1. ## Question 25876: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0051`; number: 25876 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0051/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0051/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0051.json) ## Question 25877: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0052`; number: 25877 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0052/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0052/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0052.json) ## Question 25878: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0053`; number: 25878 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0053/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0053/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0053.json) ## Question 25879: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0054`; number: 25879 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0054/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0054/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0054.json) ## Question 25880: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0055`; number: 25880 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0055/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0055/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0055.json) ## Question 25881: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0056`; number: 25881 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0056/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0056/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0056.json) ## Question 25882: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0057`; number: 25882 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0057/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0057/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0057.json) ## Question 25883: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0058`; number: 25883 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0058/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0058/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0058.json) ## Question 25884: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0059`; number: 25884 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0059/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0059/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0059.json) ## Question 25885: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0060`; number: 25885 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0060/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0060/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0060.json) ## Question 25886: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0061`; number: 25886 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0061/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0061/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0061.json) ## Question 25887: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0062`; number: 25887 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0062/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0062/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0062.json) ## Question 25888: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0063`; number: 25888 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0063/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0063/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0063.json) ## Question 25889: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0064`; number: 25889 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0064/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0064/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0064.json) ## Question 25890: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0065`; number: 25890 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0065/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0065/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0065.json) ## Question 25891: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0066`; number: 25891 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0066/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0066/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0066.json) ## Question 25892: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0067`; number: 25892 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0067/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0067/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0067.json) ## Question 25893: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0068`; number: 25893 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0068/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0068/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0068.json) ## Question 25894: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0069`; number: 25894 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0069/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0069/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0069.json) ## Question 25895: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0070`; number: 25895 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0070/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0070/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0070.json) ## Question 25896: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0071`; number: 25896 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0071/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0071/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0071.json) ## Question 25897: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0072`; number: 25897 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0072/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0072/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0072.json) ## Question 25898: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0073`; number: 25898 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0073/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0073/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0073.json) ## Question 25899: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0074`; number: 25899 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0074/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0074/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0074.json) ## Question 25900: A Feasible Zero-Gap Pair Certifies Both Primal and Dual Optimality - ID: `q-20261015-advance-20261115-r04-linear-program-duality-0075`; number: 25900 - Processing: second_context_reviewed - MKO: [mko-linear-program-duality](/en/mko/mko-linear-program-duality/) - Family: [qf-mod46-lpdual-zero-gap-certificate](/en/explore/?family=qf-mod46-lpdual-zero-gap-certificate) - Batch: [batch-20261015-advance-20261115-r04-linear-program-duality-foundations](/en/explore/?batch=batch-20261015-advance-20261115-r04-linear-program-duality-foundations) - [Derivation](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0075/) / [Markdown](/en/questions/q-20261015-advance-20261115-r04-linear-program-duality-0075/index.md) / [JSON](/data/question-derivations/questions/q-20261015-advance-20261115-r04-linear-program-duality-0075.json)