# Complete Finite Feasibility and All Tied Optimizers

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This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.

batch-20261013-advance-20261020-r04-optimization-problem-foundations · 2026-10-13 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-10, -8, 12, 0], feasible=[true, true, false, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([-10, -8, 12, 0], [Yes, Yes, No, Yes], [0, 1, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-10, -8, 12, 0], [Yes, Yes, No, Yes], [0, 1, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0001/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 2. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-9, -5, 11, 1], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([-9, -5, 11, 1], [Yes, No, Yes, Yes], [0, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-9, -5, 11, 1], [Yes, No, Yes, Yes], [0, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0002/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 3. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-8, -2, 10, 2], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([-8, -2, 10, 2], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-8, -2, 10, 2], [Yes, Yes, Yes, Yes], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0003/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 4. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-7, 1, 9, 3], feasible=[true, false, false, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([-7, 1, 9, 3], [Yes, No, No, Yes], [0, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-7, 1, 9, 3], [Yes, No, No, Yes], [0, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0004/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 5. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-6, 4, 8, 4], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([-6, 4, 8, 4], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-6, 4, 8, 4], [Yes, Yes, Yes, Yes], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0005/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 6. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-5, 7, 7, 0], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([-5, 7, 7, 0], [Yes, No, Yes, Yes], [0, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-5, 7, 7, 0], [Yes, No, Yes, Yes], [0, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0006/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 7. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-4, -7, 6, 1], feasible=[true, true, false, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([-4, -7, 6, 1], [Yes, Yes, No, Yes], [0, 1, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-4, -7, 6, 1], [Yes, Yes, No, Yes], [0, 1, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0007/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 8. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-3, -4, 5, 2], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([-3, -4, 5, 2], [Yes, No, Yes, Yes], [0, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-3, -4, 5, 2], [Yes, No, Yes, Yes], [0, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0008/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 9. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-2, -1, 4, 3], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([-2, -1, 4, 3], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-2, -1, 4, 3], [Yes, Yes, Yes, Yes], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0009/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 10. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-1, 2, 3, 4], feasible=[true, false, false, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([-1, 2, 3, 4], [Yes, No, No, Yes], [0, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-1, 2, 3, 4], [Yes, No, No, Yes], [0, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0010/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 11. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[0, 5, 2, 0], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([0, 5, 2, 0], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([0, 5, 2, 0], [Yes, Yes, Yes, Yes], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0011/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 12. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[1, 8, 1, 1], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([1, 8, 1, 1], [Yes, No, Yes, Yes], [0, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 8, 1, 1], [Yes, No, Yes, Yes], [0, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0012/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 13. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[2, -6, 0, 2], feasible=[true, true, false, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([2, -6, 0, 2], [Yes, Yes, No, Yes], [0, 1, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, -6, 0, 2], [Yes, Yes, No, Yes], [0, 1, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0013/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 14. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[3, -3, -1, 3], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([3, -3, -1, 3], [Yes, No, Yes, Yes], [0, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, -3, -1, 3], [Yes, No, Yes, Yes], [0, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0014/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 15. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[4, 0, -2, 4], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([4, 0, -2, 4], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([4, 0, -2, 4], [Yes, Yes, Yes, Yes], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0015/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 16. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[5, 3, -3, 0], feasible=[true, false, false, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([5, 3, -3, 0], [Yes, No, No, Yes], [0, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([5, 3, -3, 0], [Yes, No, No, Yes], [0, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0016/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 17. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[6, 6, -4, 1], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([6, 6, -4, 1], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([6, 6, -4, 1], [Yes, Yes, Yes, Yes], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0017/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 18. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[7, -8, -5, 2], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([7, -8, -5, 2], [Yes, No, Yes, Yes], [0, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([7, -8, -5, 2], [Yes, No, Yes, Yes], [0, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0018/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 19. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[8, -5, -6, 3], feasible=[true, true, false, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([8, -5, -6, 3], [Yes, Yes, No, Yes], [0, 1, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([8, -5, -6, 3], [Yes, Yes, No, Yes], [0, 1, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0019/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 20. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[9, -2, -7, 4], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([9, -2, -7, 4], [Yes, No, Yes, Yes], [0, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([9, -2, -7, 4], [Yes, No, Yes, Yes], [0, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0020/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 21. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[10, 1, -8, 0], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([10, 1, -8, 0], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([10, 1, -8, 0], [Yes, Yes, Yes, Yes], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0021/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 22. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[11, 4, -9, 1], feasible=[true, false, false, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([11, 4, -9, 1], [Yes, No, No, Yes], [0, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([11, 4, -9, 1], [Yes, No, No, Yes], [0, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0022/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 23. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[12, 7, -10, 2], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([12, 7, -10, 2], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([12, 7, -10, 2], [Yes, Yes, Yes, Yes], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0023/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 24. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[13, -7, -11, 3], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([13, -7, -11, 3], [Yes, No, Yes, Yes], [0, 2, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([13, -7, -11, 3], [Yes, No, Yes, Yes], [0, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0024/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 25. Feasible Original Indices before Objective Comparison

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[14, -4, -12, 4], feasible=[true, true, false, true]. Give (all values, feasible mask, every feasible original index).

View answer and explanation([14, -4, -12, 4], [Yes, Yes, No, Yes], [0, 1, 3])

Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([14, -4, -12, 4], [Yes, Yes, No, Yes], [0, 1, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0025/)

Optimization problem · qf-app20-optimization-feasible-filter · candidate





## 26. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-10, -8, 12, 0], feasible=[true, true, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([-10, -8, 12, 0], [Yes, Yes, No, Yes], min, -10, [0])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-10, -8, 12, 0], [Yes, Yes, No, Yes], min, -10, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0026/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 27. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-9, -5, 11, 1], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([-9, -5, 11, 1], [Yes, No, Yes, Yes], min, -9, [0])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-9, -5, 11, 1], [Yes, No, Yes, Yes], min, -9, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0027/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 28. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-8, -2, 10, 2], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([-8, -2, 10, 2], [Yes, Yes, Yes, Yes], min, -8, [0])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-8, -2, 10, 2], [Yes, Yes, Yes, Yes], min, -8, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0028/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 29. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-7, 1, 9, 3], feasible=[true, false, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([-7, 1, 9, 3], [Yes, No, No, Yes], min, -7, [0])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-7, 1, 9, 3], [Yes, No, No, Yes], min, -7, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0029/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 30. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-6, 4, 8, 4], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([-6, 4, 8, 4], [Yes, Yes, Yes, Yes], min, -6, [0])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-6, 4, 8, 4], [Yes, Yes, Yes, Yes], min, -6, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0030/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 31. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-5, 7, 7, 0], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([-5, 7, 7, 0], [Yes, No, Yes, Yes], min, -5, [0])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-5, 7, 7, 0], [Yes, No, Yes, Yes], min, -5, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0031/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 32. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-4, -7, 6, 1], feasible=[true, true, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([-4, -7, 6, 1], [Yes, Yes, No, Yes], min, -7, [1])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-4, -7, 6, 1], [Yes, Yes, No, Yes], min, -7, [1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0032/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 33. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-3, -4, 5, 2], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([-3, -4, 5, 2], [Yes, No, Yes, Yes], min, -3, [0])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-3, -4, 5, 2], [Yes, No, Yes, Yes], min, -3, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0033/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 34. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-2, -1, 4, 3], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([-2, -1, 4, 3], [Yes, Yes, Yes, Yes], min, -2, [0])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-2, -1, 4, 3], [Yes, Yes, Yes, Yes], min, -2, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0034/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 35. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-1, 2, 3, 4], feasible=[true, false, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([-1, 2, 3, 4], [Yes, No, No, Yes], min, -1, [0])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-1, 2, 3, 4], [Yes, No, No, Yes], min, -1, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0035/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 36. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[0, 5, 2, 0], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([0, 5, 2, 0], [Yes, Yes, Yes, Yes], min, 0, [0, 3])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([0, 5, 2, 0], [Yes, Yes, Yes, Yes], min, 0, [0, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0036/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 37. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[1, 8, 1, 1], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([1, 8, 1, 1], [Yes, No, Yes, Yes], min, 1, [0, 2, 3])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 8, 1, 1], [Yes, No, Yes, Yes], min, 1, [0, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0037/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 38. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[2, -6, 0, 2], feasible=[true, true, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([2, -6, 0, 2], [Yes, Yes, No, Yes], min, -6, [1])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, -6, 0, 2], [Yes, Yes, No, Yes], min, -6, [1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0038/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 39. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[3, -3, -1, 3], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([3, -3, -1, 3], [Yes, No, Yes, Yes], min, -1, [2])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, -3, -1, 3], [Yes, No, Yes, Yes], min, -1, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0039/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 40. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[4, 0, -2, 4], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([4, 0, -2, 4], [Yes, Yes, Yes, Yes], min, -2, [2])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([4, 0, -2, 4], [Yes, Yes, Yes, Yes], min, -2, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0040/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 41. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[5, 3, -3, 0], feasible=[true, false, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([5, 3, -3, 0], [Yes, No, No, Yes], min, 0, [3])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([5, 3, -3, 0], [Yes, No, No, Yes], min, 0, [3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0041/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 42. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[6, 6, -4, 1], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([6, 6, -4, 1], [Yes, Yes, Yes, Yes], min, -4, [2])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([6, 6, -4, 1], [Yes, Yes, Yes, Yes], min, -4, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0042/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 43. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[7, -8, -5, 2], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([7, -8, -5, 2], [Yes, No, Yes, Yes], min, -5, [2])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([7, -8, -5, 2], [Yes, No, Yes, Yes], min, -5, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0043/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 44. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[8, -5, -6, 3], feasible=[true, true, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([8, -5, -6, 3], [Yes, Yes, No, Yes], min, -5, [1])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([8, -5, -6, 3], [Yes, Yes, No, Yes], min, -5, [1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0044/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 45. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[9, -2, -7, 4], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([9, -2, -7, 4], [Yes, No, Yes, Yes], min, -7, [2])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([9, -2, -7, 4], [Yes, No, Yes, Yes], min, -7, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0045/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 46. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[10, 1, -8, 0], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([10, 1, -8, 0], [Yes, Yes, Yes, Yes], min, -8, [2])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([10, 1, -8, 0], [Yes, Yes, Yes, Yes], min, -8, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0046/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 47. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[11, 4, -9, 1], feasible=[true, false, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([11, 4, -9, 1], [Yes, No, No, Yes], min, 1, [3])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([11, 4, -9, 1], [Yes, No, No, Yes], min, 1, [3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0047/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 48. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[12, 7, -10, 2], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([12, 7, -10, 2], [Yes, Yes, Yes, Yes], min, -10, [2])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([12, 7, -10, 2], [Yes, Yes, Yes, Yes], min, -10, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0048/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 49. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[13, -7, -11, 3], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([13, -7, -11, 3], [Yes, No, Yes, Yes], min, -11, [2])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([13, -7, -11, 3], [Yes, No, Yes, Yes], min, -11, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0049/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 50. Finite Minimum Value and Every Original Minimizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[14, -4, -12, 4], feasible=[true, true, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).

View answer and explanation([14, -4, -12, 4], [Yes, Yes, No, Yes], min, -4, [1])

Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([14, -4, -12, 4], [Yes, Yes, No, Yes], min, -4, [1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0050/)

Optimization problem · qf-app20-optimization-argmin · candidate





## 51. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-10, -8, 12, 0], feasible=[true, true, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([-10, -8, 12, 0], [Yes, Yes, No, Yes], max, 0, [3])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-10, -8, 12, 0], [Yes, Yes, No, Yes], max, 0, [3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0051/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 52. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-9, -5, 11, 1], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([-9, -5, 11, 1], [Yes, No, Yes, Yes], max, 11, [2])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-9, -5, 11, 1], [Yes, No, Yes, Yes], max, 11, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0052/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 53. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-8, -2, 10, 2], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([-8, -2, 10, 2], [Yes, Yes, Yes, Yes], max, 10, [2])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-8, -2, 10, 2], [Yes, Yes, Yes, Yes], max, 10, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0053/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 54. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-7, 1, 9, 3], feasible=[true, false, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([-7, 1, 9, 3], [Yes, No, No, Yes], max, 3, [3])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-7, 1, 9, 3], [Yes, No, No, Yes], max, 3, [3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0054/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 55. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-6, 4, 8, 4], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([-6, 4, 8, 4], [Yes, Yes, Yes, Yes], max, 8, [2])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-6, 4, 8, 4], [Yes, Yes, Yes, Yes], max, 8, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0055/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 56. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-5, 7, 7, 0], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([-5, 7, 7, 0], [Yes, No, Yes, Yes], max, 7, [2])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-5, 7, 7, 0], [Yes, No, Yes, Yes], max, 7, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0056/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 57. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-4, -7, 6, 1], feasible=[true, true, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([-4, -7, 6, 1], [Yes, Yes, No, Yes], max, 1, [3])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-4, -7, 6, 1], [Yes, Yes, No, Yes], max, 1, [3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0057/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 58. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-3, -4, 5, 2], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([-3, -4, 5, 2], [Yes, No, Yes, Yes], max, 5, [2])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-3, -4, 5, 2], [Yes, No, Yes, Yes], max, 5, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0058/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 59. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-2, -1, 4, 3], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([-2, -1, 4, 3], [Yes, Yes, Yes, Yes], max, 4, [2])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-2, -1, 4, 3], [Yes, Yes, Yes, Yes], max, 4, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0059/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 60. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-1, 2, 3, 4], feasible=[true, false, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([-1, 2, 3, 4], [Yes, No, No, Yes], max, 4, [3])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-1, 2, 3, 4], [Yes, No, No, Yes], max, 4, [3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0060/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 61. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[0, 5, 2, 0], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([0, 5, 2, 0], [Yes, Yes, Yes, Yes], max, 5, [1])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([0, 5, 2, 0], [Yes, Yes, Yes, Yes], max, 5, [1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0061/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 62. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[1, 8, 1, 1], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([1, 8, 1, 1], [Yes, No, Yes, Yes], max, 1, [0, 2, 3])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 8, 1, 1], [Yes, No, Yes, Yes], max, 1, [0, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0062/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 63. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[2, -6, 0, 2], feasible=[true, true, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([2, -6, 0, 2], [Yes, Yes, No, Yes], max, 2, [0, 3])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, -6, 0, 2], [Yes, Yes, No, Yes], max, 2, [0, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0063/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 64. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[3, -3, -1, 3], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([3, -3, -1, 3], [Yes, No, Yes, Yes], max, 3, [0, 3])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, -3, -1, 3], [Yes, No, Yes, Yes], max, 3, [0, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0064/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 65. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[4, 0, -2, 4], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([4, 0, -2, 4], [Yes, Yes, Yes, Yes], max, 4, [0, 3])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([4, 0, -2, 4], [Yes, Yes, Yes, Yes], max, 4, [0, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0065/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 66. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[5, 3, -3, 0], feasible=[true, false, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([5, 3, -3, 0], [Yes, No, No, Yes], max, 5, [0])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([5, 3, -3, 0], [Yes, No, No, Yes], max, 5, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0066/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 67. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[6, 6, -4, 1], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([6, 6, -4, 1], [Yes, Yes, Yes, Yes], max, 6, [0, 1])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([6, 6, -4, 1], [Yes, Yes, Yes, Yes], max, 6, [0, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0067/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 68. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[7, -8, -5, 2], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([7, -8, -5, 2], [Yes, No, Yes, Yes], max, 7, [0])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([7, -8, -5, 2], [Yes, No, Yes, Yes], max, 7, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0068/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 69. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[8, -5, -6, 3], feasible=[true, true, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([8, -5, -6, 3], [Yes, Yes, No, Yes], max, 8, [0])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([8, -5, -6, 3], [Yes, Yes, No, Yes], max, 8, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0069/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 70. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[9, -2, -7, 4], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([9, -2, -7, 4], [Yes, No, Yes, Yes], max, 9, [0])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([9, -2, -7, 4], [Yes, No, Yes, Yes], max, 9, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0070/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 71. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[10, 1, -8, 0], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([10, 1, -8, 0], [Yes, Yes, Yes, Yes], max, 10, [0])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([10, 1, -8, 0], [Yes, Yes, Yes, Yes], max, 10, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0071/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 72. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[11, 4, -9, 1], feasible=[true, false, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([11, 4, -9, 1], [Yes, No, No, Yes], max, 11, [0])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([11, 4, -9, 1], [Yes, No, No, Yes], max, 11, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0072/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 73. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[12, 7, -10, 2], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([12, 7, -10, 2], [Yes, Yes, Yes, Yes], max, 12, [0])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([12, 7, -10, 2], [Yes, Yes, Yes, Yes], max, 12, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0073/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 74. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[13, -7, -11, 3], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([13, -7, -11, 3], [Yes, No, Yes, Yes], max, 13, [0])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([13, -7, -11, 3], [Yes, No, Yes, Yes], max, 13, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0074/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 75. Finite Maximum Value and Every Original Maximizer Index

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[14, -4, -12, 4], feasible=[true, true, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).

View answer and explanation([14, -4, -12, 4], [Yes, Yes, No, Yes], max, 14, [0])

Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([14, -4, -12, 4], [Yes, Yes, No, Yes], max, 14, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0075/)

Optimization problem · qf-app20-optimization-argmax · candidate





## 76. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 0], [2, 0], [3, 0]], constraint [A,B,c]=[1, 1, 5] means A*x+B*y≤c, objective [u,v]=[-2, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([1, 1, 5], [-2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 0, Yes, -4], [3, 3, 0, Yes, -6]], 0, [0])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 5], [-2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 0, Yes, -4], [3, 3, 0, Yes, -6]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0076/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 77. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 1], [2, 2], [3, 1]], constraint [A,B,c]=[2, 1, 6] means A*x+B*y≤c, objective [u,v]=[-1, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([2, 1, 6], [-1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 2, Yes, 2], [3, 3, 1, No, -1]], 0, [0])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 6], [-1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 2, Yes, 2], [3, 3, 1, No, -1]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0077/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 78. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 2], [2, 4], [3, 2]], constraint [A,B,c]=[3, 1, 7] means A*x+B*y≤c, objective [u,v]=[0, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([3, 1, 7], [0, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 4, No, 8], [3, 3, 2, No, 4]], 4, [1])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 7], [0, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 4, No, 8], [3, 3, 2, No, 4]], 4, [1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0078/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 79. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 3], [2, 6], [3, 3]], constraint [A,B,c]=[1, 1, 8] means A*x+B*y≤c, objective [u,v]=[1, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([1, 1, 8], [1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 6, Yes, 14], [3, 3, 3, Yes, 9]], 0, [0])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 8], [1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 6, Yes, 14], [3, 3, 3, Yes, 9]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0079/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 80. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 4], [2, 1], [3, 0]], constraint [A,B,c]=[2, 1, 9] means A*x+B*y≤c, objective [u,v]=[2, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([2, 1, 9], [2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 1, Yes, 6], [3, 3, 0, Yes, 6]], 10, [1])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 9], [2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 1, Yes, 6], [3, 3, 0, Yes, 6]], 10, [1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0080/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 81. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 0], [2, 3], [3, 1]], constraint [A,B,c]=[3, 1, 10] means A*x+B*y≤c, objective [u,v]=[-2, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([3, 1, 10], [-2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 3, Yes, 2], [3, 3, 1, Yes, -4]], -4, [3])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 10], [-2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 3, Yes, 2], [3, 3, 1, Yes, -4]], -4, [3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0081/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 82. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 1], [2, 5], [3, 2]], constraint [A,B,c]=[1, 1, 11] means A*x+B*y≤c, objective [u,v]=[-1, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([1, 1, 11], [-1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 5, Yes, 8], [3, 3, 2, Yes, 1]], 8, [2])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 11], [-1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 5, Yes, 8], [3, 3, 2, Yes, 1]], 8, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0082/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 83. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 2], [2, 0], [3, 3]], constraint [A,B,c]=[2, 1, 12] means A*x+B*y≤c, objective [u,v]=[0, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([2, 1, 12], [0, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 0, Yes, 0], [3, 3, 3, Yes, 6]], 0, [0, 2])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 12], [0, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 0, Yes, 0], [3, 3, 3, Yes, 6]], 0, [0, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0083/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 84. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 3], [2, 2], [3, 0]], constraint [A,B,c]=[3, 1, 5] means A*x+B*y≤c, objective [u,v]=[1, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([3, 1, 5], [1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 3, No, 7], [2, 2, 2, No, 6], [3, 3, 0, No, 3]], 0, [0])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 5], [1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 3, No, 7], [2, 2, 2, No, 6], [3, 3, 0, No, 3]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0084/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 85. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 4], [2, 4], [3, 1]], constraint [A,B,c]=[1, 1, 6] means A*x+B*y≤c, objective [u,v]=[2, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([1, 1, 6], [2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 4, Yes, 12], [3, 3, 1, Yes, 8]], 0, [0])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 6], [2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 4, Yes, 12], [3, 3, 1, Yes, 8]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0085/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 86. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 0], [2, 6], [3, 2]], constraint [A,B,c]=[2, 1, 7] means A*x+B*y≤c, objective [u,v]=[-2, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([2, 1, 7], [-2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 6, No, 8], [3, 3, 2, No, -2]], 0, [0])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 7], [-2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 6, No, 8], [3, 3, 2, No, -2]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0086/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 87. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 1], [2, 1], [3, 3]], constraint [A,B,c]=[3, 1, 8] means A*x+B*y≤c, objective [u,v]=[-1, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([3, 1, 8], [-1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 1, Yes, 0], [3, 3, 3, No, 3]], 0, [0, 2])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 8], [-1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 1, Yes, 0], [3, 3, 3, No, 3]], 0, [0, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0087/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 88. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 2], [2, 3], [3, 0]], constraint [A,B,c]=[1, 1, 9] means A*x+B*y≤c, objective [u,v]=[0, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([1, 1, 9], [0, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 3, Yes, 6], [3, 3, 0, Yes, 0]], 6, [2])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 9], [0, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 3, Yes, 6], [3, 3, 0, Yes, 0]], 6, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0088/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 89. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 3], [2, 5], [3, 1]], constraint [A,B,c]=[2, 1, 10] means A*x+B*y≤c, objective [u,v]=[1, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([2, 1, 10], [1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 5, Yes, 12], [3, 3, 1, Yes, 5]], 0, [0])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 10], [1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 5, Yes, 12], [3, 3, 1, Yes, 5]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0089/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 90. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 4], [2, 0], [3, 2]], constraint [A,B,c]=[3, 1, 11] means A*x+B*y≤c, objective [u,v]=[2, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([3, 1, 11], [2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 0, Yes, 4], [3, 3, 2, Yes, 10]], 10, [1, 3])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 11], [2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 0, Yes, 4], [3, 3, 2, Yes, 10]], 10, [1, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0090/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 91. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 0], [2, 2], [3, 3]], constraint [A,B,c]=[1, 1, 12] means A*x+B*y≤c, objective [u,v]=[-2, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([1, 1, 12], [-2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 2, Yes, 0], [3, 3, 3, Yes, 0]], -2, [1])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 12], [-2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 2, Yes, 0], [3, 3, 3, Yes, 0]], -2, [1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0091/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 92. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 1], [2, 4], [3, 0]], constraint [A,B,c]=[2, 1, 5] means A*x+B*y≤c, objective [u,v]=[-1, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([2, 1, 5], [-1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 4, No, 6], [3, 3, 0, No, -3]], 1, [1])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 5], [-1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 4, No, 6], [3, 3, 0, No, -3]], 1, [1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0092/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 93. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 2], [2, 6], [3, 1]], constraint [A,B,c]=[3, 1, 6] means A*x+B*y≤c, objective [u,v]=[0, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([3, 1, 6], [0, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 6, No, 12], [3, 3, 1, No, 2]], 0, [0])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 6], [0, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 6, No, 12], [3, 3, 1, No, 2]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0093/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 94. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 3], [2, 1], [3, 2]], constraint [A,B,c]=[1, 1, 7] means A*x+B*y≤c, objective [u,v]=[1, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([1, 1, 7], [1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 1, Yes, 4], [3, 3, 2, Yes, 7]], 7, [1, 3])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 7], [1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 1, Yes, 4], [3, 3, 2, Yes, 7]], 7, [1, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0094/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 95. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 4], [2, 3], [3, 3]], constraint [A,B,c]=[2, 1, 8] means A*x+B*y≤c, objective [u,v]=[2, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([2, 1, 8], [2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 3, Yes, 10], [3, 3, 3, No, 12]], 0, [0])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 8], [2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 3, Yes, 10], [3, 3, 3, No, 12]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0095/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 96. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 0], [2, 5], [3, 0]], constraint [A,B,c]=[3, 1, 9] means A*x+B*y≤c, objective [u,v]=[-2, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([3, 1, 9], [-2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 5, No, 6], [3, 3, 0, Yes, -6]], 0, [0])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 9], [-2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 5, No, 6], [3, 3, 0, Yes, -6]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0096/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 97. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 1], [2, 0], [3, 1]], constraint [A,B,c]=[1, 1, 10] means A*x+B*y≤c, objective [u,v]=[-1, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([1, 1, 10], [-1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 0, Yes, -2], [3, 3, 1, Yes, -1]], -2, [2])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 10], [-1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 0, Yes, -2], [3, 3, 1, Yes, -1]], -2, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0097/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 98. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 2], [2, 2], [3, 2]], constraint [A,B,c]=[2, 1, 11] means A*x+B*y≤c, objective [u,v]=[0, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([2, 1, 11], [0, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 2, Yes, 4], [3, 3, 2, Yes, 4]], 4, [1, 2, 3])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 11], [0, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 2, Yes, 4], [3, 3, 2, Yes, 4]], 4, [1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0098/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 99. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 3], [2, 4], [3, 3]], constraint [A,B,c]=[3, 1, 12] means A*x+B*y≤c, objective [u,v]=[1, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([3, 1, 12], [1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 4, Yes, 10], [3, 3, 3, Yes, 9]], 0, [0])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 12], [1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 4, Yes, 10], [3, 3, 3, Yes, 9]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0099/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate





## 100. A Linear Constraint on a Complete Ordered Finite Point List

Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 4], [2, 6], [3, 0]], constraint [A,B,c]=[1, 1, 5] means A*x+B*y≤c, objective [u,v]=[2, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.

View answer and explanation([1, 1, 5], [2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 6, No, 16], [3, 3, 0, Yes, 6]], 10, [1])

Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 5], [2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 6, No, 16], [3, 3, 0, Yes, 6]], 10, [1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261020-r04-optimization-problem-0100/)

Optimization problem · qf-app20-optimization-linear-constraint-audit · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261020-r04-optimization-problem-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261013-advance-20261020-r04-optimization-problem-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261020-r04-optimization-problem-foundations/validation-report.json)