# Canonical Finite LP Grids, Feasibility and All Tied Optimizers

This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.

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-20261021-r06-linear-programming-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. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[0, 0], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 3]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([0, 0], [[-1, 0, 0, 0, Yes], [0, -1, 0, 0, Yes], [1, 1, 3, 0, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0001/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 2. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[1, 1], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 4]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([1, 1], [[-1, 0, 0, -1, Yes], [0, -1, 0, -1, Yes], [1, 1, 4, 2, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0002/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 3. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[2, 2], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([2, 2], [[-1, 0, 0, -2, Yes], [0, -1, 0, -2, Yes], [1, 1, 5, 4, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0003/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 4. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[3, 3], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 6]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([3, 3], [[-1, 0, 0, -3, Yes], [0, -1, 0, -3, Yes], [1, 1, 6, 6, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0004/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 5. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[4, 0], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 7]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

View answer and explanation([4, 0], [[-1, 0, 0, -4, Yes], [0, -1, 0, 0, Yes], [1, 1, 7, 4, Yes]], Yes)

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([4, 0], [[-1, 0, 0, -4, Yes], [0, -1, 0, 0, Yes], [1, 1, 7, 4, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0005/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 6. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[0, 1], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 8]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([0, 1], [[-1, 0, 0, 0, Yes], [0, -1, 0, -1, Yes], [1, 1, 8, 1, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0006/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 7. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[1, 2], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 9]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

View answer and explanation([1, 2], [[-1, 0, 0, -1, Yes], [0, -1, 0, -2, Yes], [1, 1, 9, 3, Yes]], Yes)

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([1, 2], [[-1, 0, 0, -1, Yes], [0, -1, 0, -2, Yes], [1, 1, 9, 3, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0007/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 8. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[2, 3], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 3]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([2, 3], [[-1, 0, 0, -2, Yes], [0, -1, 0, -3, Yes], [1, 1, 3, 5, No]], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0008/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 9. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[3, 0], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 4]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([3, 0], [[-1, 0, 0, -3, Yes], [0, -1, 0, 0, Yes], [1, 1, 4, 3, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0009/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 10. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[4, 1], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

View answer and explanation([4, 1], [[-1, 0, 0, -4, Yes], [0, -1, 0, -1, Yes], [1, 1, 5, 5, Yes]], Yes)

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([4, 1], [[-1, 0, 0, -4, Yes], [0, -1, 0, -1, Yes], [1, 1, 5, 5, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0010/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 11. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[0, 2], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 6]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([0, 2], [[-1, 0, 0, 0, Yes], [0, -1, 0, -2, Yes], [1, 1, 6, 2, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0011/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 12. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[1, 3], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 7]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([1, 3], [[-1, 0, 0, -1, Yes], [0, -1, 0, -3, Yes], [1, 1, 7, 4, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0012/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 13. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[2, 0], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 8]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([2, 0], [[-1, 0, 0, -2, Yes], [0, -1, 0, 0, Yes], [1, 1, 8, 2, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0013/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 14. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[3, 1], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 9]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

View answer and explanation([3, 1], [[-1, 0, 0, -3, Yes], [0, -1, 0, -1, Yes], [1, 1, 9, 4, Yes]], Yes)

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([3, 1], [[-1, 0, 0, -3, Yes], [0, -1, 0, -1, Yes], [1, 1, 9, 4, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0014/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 15. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[4, 2], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 3]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([4, 2], [[-1, 0, 0, -4, Yes], [0, -1, 0, -2, Yes], [1, 1, 3, 6, No]], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0015/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 16. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[0, 3], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 4]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([0, 3], [[-1, 0, 0, 0, Yes], [0, -1, 0, -3, Yes], [1, 1, 4, 3, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0016/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 17. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[1, 0], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([1, 0], [[-1, 0, 0, -1, Yes], [0, -1, 0, 0, Yes], [1, 1, 5, 1, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0017/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 18. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[2, 1], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 6]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([2, 1], [[-1, 0, 0, -2, Yes], [0, -1, 0, -1, Yes], [1, 1, 6, 3, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0018/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 19. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[3, 2], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 7]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([3, 2], [[-1, 0, 0, -3, Yes], [0, -1, 0, -2, Yes], [1, 1, 7, 5, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0019/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 20. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[4, 3], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 8]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

View answer and explanation([4, 3], [[-1, 0, 0, -4, Yes], [0, -1, 0, -3, Yes], [1, 1, 8, 7, Yes]], Yes)

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([4, 3], [[-1, 0, 0, -4, Yes], [0, -1, 0, -3, Yes], [1, 1, 8, 7, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0020/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 21. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[0, 0], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 9]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

View answer and explanation([0, 0], [[-1, 0, 0, 0, Yes], [0, -1, 0, 0, Yes], [1, 1, 9, 0, Yes]], Yes)

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([0, 0], [[-1, 0, 0, 0, Yes], [0, -1, 0, 0, Yes], [1, 1, 9, 0, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0021/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 22. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[1, 1], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 3]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([1, 1], [[-1, 0, 0, -1, Yes], [0, -1, 0, -1, Yes], [1, 1, 3, 2, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0022/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 23. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[2, 2], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 4]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([2, 2], [[-1, 0, 0, -2, Yes], [0, -1, 0, -2, Yes], [1, 1, 4, 4, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0023/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 24. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[3, 3], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([3, 3], [[-1, 0, 0, -3, Yes], [0, -1, 0, -3, Yes], [1, 1, 5, 6, No]], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0024/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 25. Every Constraint at One Declared Point

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. point=[4, 0], constraints [A,B,c]=[[-1, 0, 0], [0, -1, 0], [1, 1, 6]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (point,every [A,B,c,A*x+B*y,satisfies?] row,all constraints hold?).

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

Check each inequality including equality at the boundary; infeasible candidates cannot be optimizers merely because their objective is better. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([4, 0], [[-1, 0, 0, -4, Yes], [0, -1, 0, 0, Yes], [1, 1, 6, 4, Yes]], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0025/)

Linear programming · qf-app21-lp-constraint-row-audit · candidate





## 26. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 0], [0, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 3]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 0, 2, [Yes, Yes, Yes], Yes, null], [2, 1, 0, [Yes, Yes, Yes], Yes, null], [3, 2, 0, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0026/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 27. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 1], [1, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 4]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 1, [Yes, Yes, Yes], Yes, null], [2, 1, 2, [Yes, Yes, Yes], Yes, null], [3, 2, 1, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0027/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 28. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 2], [2, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 2, [Yes, Yes, Yes], Yes, null], [2, 2, 2, [Yes, Yes, Yes], Yes, null]], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0028/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 29. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 3], [3, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 6]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 3, [Yes, Yes, Yes], Yes, null], [2, 2, 3, [Yes, Yes, Yes], Yes, null], [3, 3, 2, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0029/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 30. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 4], [4, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 7]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 0, [Yes, Yes, Yes], Yes, null], [2, 2, 4, [Yes, Yes, Yes], Yes, null], [3, 4, 2, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0030/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 31. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 0], [5, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 8]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 1, [Yes, Yes, Yes], Yes, null], [2, 2, 0, [Yes, Yes, Yes], Yes, null], [3, 5, 2, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0031/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 32. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 1], [0, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 9]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

View answer and explanation([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 0, 2, [Yes, Yes, Yes], Yes, null], [2, 1, 2, [Yes, Yes, Yes], Yes, null], [3, 2, 1, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3])

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 0, 2, [Yes, Yes, Yes], Yes, null], [2, 1, 2, [Yes, Yes, Yes], Yes, null], [3, 2, 1, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0032/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 33. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 2], [1, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 3]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 2, [Yes, Yes, Yes], Yes, null], [2, 1, 3, [Yes, Yes, No], No, null], [3, 2, 2, [Yes, Yes, No], No, null]], [0, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0033/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 34. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 3], [2, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 4]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 0, [Yes, Yes, Yes], Yes, null], [2, 2, 2, [Yes, Yes, Yes], Yes, null], [3, 2, 3, [Yes, Yes, No], No, null]], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0034/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 35. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 4], [3, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 1, [Yes, Yes, Yes], Yes, null], [2, 2, 4, [Yes, Yes, No], No, null], [3, 3, 2, [Yes, Yes, Yes], Yes, null]], [0, 1, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0035/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 36. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 0], [4, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 6]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 2, [Yes, Yes, Yes], Yes, null], [2, 2, 0, [Yes, Yes, Yes], Yes, null], [3, 4, 2, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0036/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 37. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 1], [5, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 7]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

View answer and explanation([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 3, [Yes, Yes, Yes], Yes, null], [2, 2, 1, [Yes, Yes, Yes], Yes, null], [3, 5, 2, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3])

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 3, [Yes, Yes, Yes], Yes, null], [2, 2, 1, [Yes, Yes, Yes], Yes, null], [3, 5, 2, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0037/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 38. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 2], [0, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 8]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 0, 2, [Yes, Yes, Yes], Yes, null], [2, 1, 0, [Yes, Yes, Yes], Yes, null], [3, 2, 2, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0038/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 39. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 3], [1, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 9]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

View answer and explanation([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 1, [Yes, Yes, Yes], Yes, null], [2, 1, 2, [Yes, Yes, Yes], Yes, null], [3, 2, 3, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3])

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 1, [Yes, Yes, Yes], Yes, null], [2, 1, 2, [Yes, Yes, Yes], Yes, null], [3, 2, 3, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0039/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 40. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 4], [2, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 3]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 2, [Yes, Yes, Yes], Yes, null], [2, 2, 2, [Yes, Yes, No], No, null], [3, 2, 4, [Yes, Yes, No], No, null]], [0, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0040/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 41. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 0], [3, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 4]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 3, [Yes, Yes, Yes], Yes, null], [2, 2, 0, [Yes, Yes, Yes], Yes, null], [3, 3, 2, [Yes, Yes, No], No, null]], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0041/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 42. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 1], [4, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 0, [Yes, Yes, Yes], Yes, null], [2, 2, 1, [Yes, Yes, Yes], Yes, null], [3, 4, 2, [Yes, Yes, No], No, null]], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0042/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 43. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 2], [5, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 6]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 1, [Yes, Yes, Yes], Yes, null], [2, 2, 2, [Yes, Yes, Yes], Yes, null], [3, 5, 2, [Yes, Yes, No], No, null]], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0043/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 44. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 3], [0, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 7]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 0, 2, [Yes, Yes, Yes], Yes, null], [2, 1, 2, [Yes, Yes, Yes], Yes, null], [3, 2, 3, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0044/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 45. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 4], [1, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 8]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 2, [Yes, Yes, Yes], Yes, null], [2, 1, 3, [Yes, Yes, Yes], Yes, null], [3, 2, 4, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0045/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 46. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 0], [2, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 9]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

View answer and explanation([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 0, [Yes, Yes, Yes], Yes, null], [2, 2, 0, [Yes, Yes, Yes], Yes, null], [3, 2, 2, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3])

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 0, [Yes, Yes, Yes], Yes, null], [2, 2, 0, [Yes, Yes, Yes], Yes, null], [3, 2, 2, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0046/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 47. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 1], [3, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 3]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 1, [Yes, Yes, Yes], Yes, null], [2, 2, 1, [Yes, Yes, Yes], Yes, null], [3, 3, 2, [Yes, Yes, No], No, null]], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0047/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 48. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 2], [4, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 4]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 2, [Yes, Yes, Yes], Yes, null], [2, 2, 2, [Yes, Yes, Yes], Yes, null], [3, 4, 2, [Yes, Yes, No], No, null]], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0048/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 49. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 3], [5, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 1, 3, [Yes, Yes, Yes], Yes, null], [2, 2, 3, [Yes, Yes, Yes], Yes, null], [3, 5, 2, [Yes, Yes, No], No, null]], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0049/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 50. Feasible Indices in Canonical Candidate-Grid Order

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 4], [0, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 6]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical constraints,every [index,x,y,constraint truth list,all constraints hold?,null] row,feasible canonical indices). Here null records that no objective was supplied.

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

Keep the per-constraint truth list as well as overall feasibility. Canonical indices are not the original input positions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [[0, 0, 0, [Yes, Yes, Yes], Yes, null], [1, 0, 2, [Yes, Yes, Yes], Yes, null], [2, 1, 0, [Yes, Yes, Yes], Yes, null], [3, 2, 4, [Yes, Yes, Yes], Yes, null]], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0050/)

Linear programming · qf-app21-lp-feasible-inventory · candidate





## 51. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 0], [0, 2]], objective [u,v]=[-2, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([-2, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 0, -2], [3, 2, 0, -4]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0051/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 52. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 1], [1, 2]], objective [u,v]=[-1, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([-1, 2], [[0, 0, 0, 0], [1, 1, 1, 1], [2, 1, 2, 3], [3, 2, 1, 0]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0052/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 53. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 2], [2, 2]], objective [u,v]=[0, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([0, 2], [[0, 0, 0, 0], [1, 1, 2, 4], [2, 2, 2, 4]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0053/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 54. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 3], [3, 2]], objective [u,v]=[1, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

View answer and explanation([1, 2], [[0, 0, 0, 0], [1, 1, 3, 7], [2, 2, 3, 8], [3, 3, 2, 7]])

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([1, 2], [[0, 0, 0, 0], [1, 1, 3, 7], [2, 2, 3, 8], [3, 3, 2, 7]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0054/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 55. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 4], [4, 2]], objective [u,v]=[2, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([2, 2], [[0, 0, 0, 0], [1, 1, 0, 2], [2, 2, 4, 12], [3, 4, 2, 12]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0055/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 56. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 0], [5, 2]], objective [u,v]=[-2, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([-2, 2], [[0, 0, 0, 0], [1, 1, 1, 0], [2, 2, 0, -4], [3, 5, 2, -6]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0056/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 57. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 1], [0, 2]], objective [u,v]=[-1, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([-1, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 2, 3], [3, 2, 1, 0]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0057/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 58. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 2], [1, 2]], objective [u,v]=[0, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([0, 2], [[0, 0, 0, 0], [1, 1, 2, 4], [2, 1, 3, 6], [3, 2, 2, 4]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0058/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 59. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 3], [2, 2]], objective [u,v]=[1, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([1, 2], [[0, 0, 0, 0], [1, 1, 0, 1], [2, 2, 2, 6], [3, 2, 3, 8]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0059/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 60. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 4], [3, 2]], objective [u,v]=[2, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([2, 2], [[0, 0, 0, 0], [1, 1, 1, 4], [2, 2, 4, 12], [3, 3, 2, 10]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0060/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 61. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 0], [4, 2]], objective [u,v]=[-2, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([-2, 2], [[0, 0, 0, 0], [1, 1, 2, 2], [2, 2, 0, -4], [3, 4, 2, -4]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0061/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 62. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 1], [5, 2]], objective [u,v]=[-1, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([-1, 2], [[0, 0, 0, 0], [1, 1, 3, 5], [2, 2, 1, 0], [3, 5, 2, -1]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0062/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 63. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 2], [0, 2]], objective [u,v]=[0, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([0, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 0, 0], [3, 2, 2, 4]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0063/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 64. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 3], [1, 2]], objective [u,v]=[1, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

View answer and explanation([1, 2], [[0, 0, 0, 0], [1, 1, 1, 3], [2, 1, 2, 5], [3, 2, 3, 8]])

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([1, 2], [[0, 0, 0, 0], [1, 1, 1, 3], [2, 1, 2, 5], [3, 2, 3, 8]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0064/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 65. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 4], [2, 2]], objective [u,v]=[2, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([2, 2], [[0, 0, 0, 0], [1, 1, 2, 6], [2, 2, 2, 8], [3, 2, 4, 12]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0065/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 66. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 0], [3, 2]], objective [u,v]=[-2, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([-2, 2], [[0, 0, 0, 0], [1, 1, 3, 4], [2, 2, 0, -4], [3, 3, 2, -2]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0066/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 67. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 1], [4, 2]], objective [u,v]=[-1, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([-1, 2], [[0, 0, 0, 0], [1, 1, 0, -1], [2, 2, 1, 0], [3, 4, 2, 0]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0067/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 68. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 2], [5, 2]], objective [u,v]=[0, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

View answer and explanation([0, 2], [[0, 0, 0, 0], [1, 1, 1, 2], [2, 2, 2, 4], [3, 5, 2, 4]])

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([0, 2], [[0, 0, 0, 0], [1, 1, 1, 2], [2, 2, 2, 4], [3, 5, 2, 4]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0068/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 69. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 3], [0, 2]], objective [u,v]=[1, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

View answer and explanation([1, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 2, 5], [3, 2, 3, 8]])

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([1, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 2, 5], [3, 2, 3, 8]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0069/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 70. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 4], [1, 2]], objective [u,v]=[2, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([2, 2], [[0, 0, 0, 0], [1, 1, 2, 6], [2, 1, 3, 8], [3, 2, 4, 12]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0070/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 71. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 0], [2, 2]], objective [u,v]=[-2, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([-2, 2], [[0, 0, 0, 0], [1, 1, 0, -2], [2, 2, 0, -4], [3, 2, 2, 0]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0071/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 72. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 1], [3, 2]], objective [u,v]=[-1, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([-1, 2], [[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 1, 0], [3, 3, 2, 1]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0072/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 73. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 2], [4, 2]], objective [u,v]=[0, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([0, 2], [[0, 0, 0, 0], [1, 1, 2, 4], [2, 2, 2, 4], [3, 4, 2, 4]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0073/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 74. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 3], [5, 2]], objective [u,v]=[1, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

View answer and explanation([1, 2], [[0, 0, 0, 0], [1, 1, 3, 7], [2, 2, 3, 8], [3, 5, 2, 9]])

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([1, 2], [[0, 0, 0, 0], [1, 1, 3, 7], [2, 2, 3, 8], [3, 5, 2, 9]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0074/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 75. A Linear Objective Does Not by Itself Establish Feasibility

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 4], [0, 2]], objective [u,v]=[2, 2]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (objective,every [canonical index,x,y,u*x+v*y] row). No constraints are checked in this family.

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

Evaluate the linear form at each distinct canonical point; do not invent feasibility or an optimum when the requested task is only objective evaluation. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([2, 2], [[0, 0, 0, 0], [1, 0, 2, 4], [2, 1, 0, 2], [3, 2, 4, 12]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0075/)

Linear programming · qf-app21-lp-objective-audit · candidate





## 76. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 0], [0, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 3]], objective=[-2, 2], direction=max. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [-2, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 0, 2, [Yes, Yes, Yes], Yes, 4], [2, 1, 0, [Yes, Yes, Yes], Yes, -2], [3, 2, 0, [Yes, Yes, Yes], Yes, -4]], 4, [1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0076/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 77. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 1], [1, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 4]], objective=[-1, 2], direction=min. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [-1, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 1, [Yes, Yes, Yes], Yes, 1], [2, 1, 2, [Yes, Yes, Yes], Yes, 3], [3, 2, 1, [Yes, Yes, Yes], Yes, 0]], 0, [0, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0077/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 78. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 2], [2, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 5]], objective=[0, 2], direction=max. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [0, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 2, [Yes, Yes, Yes], Yes, 4], [2, 2, 2, [Yes, Yes, Yes], Yes, 4]], 4, [1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0078/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 79. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 3], [3, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 6]], objective=[1, 2], direction=min. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [1, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 3, [Yes, Yes, Yes], Yes, 7], [2, 2, 3, [Yes, Yes, Yes], Yes, 8], [3, 3, 2, [Yes, Yes, Yes], Yes, 7]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0079/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 80. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 4], [4, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 7]], objective=[2, 2], direction=max. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

View answer and explanation([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [2, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 0, [Yes, Yes, Yes], Yes, 2], [2, 2, 4, [Yes, Yes, Yes], Yes, 12], [3, 4, 2, [Yes, Yes, Yes], Yes, 12]], 12, [2, 3])

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [2, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 0, [Yes, Yes, Yes], Yes, 2], [2, 2, 4, [Yes, Yes, Yes], Yes, 12], [3, 4, 2, [Yes, Yes, Yes], Yes, 12]], 12, [2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0080/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 81. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 0], [5, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 8]], objective=[-2, 2], direction=min. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

View answer and explanation([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [-2, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 1, [Yes, Yes, Yes], Yes, 0], [2, 2, 0, [Yes, Yes, Yes], Yes, -4], [3, 5, 2, [Yes, Yes, Yes], Yes, -6]], -6, [3])

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [-2, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 1, [Yes, Yes, Yes], Yes, 0], [2, 2, 0, [Yes, Yes, Yes], Yes, -4], [3, 5, 2, [Yes, Yes, Yes], Yes, -6]], -6, [3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0081/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 82. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 1], [0, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 9]], objective=[-1, 2], direction=max. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [-1, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 0, 2, [Yes, Yes, Yes], Yes, 4], [2, 1, 2, [Yes, Yes, Yes], Yes, 3], [3, 2, 1, [Yes, Yes, Yes], Yes, 0]], 4, [1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0082/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 83. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 2], [1, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 3]], objective=[0, 2], direction=min. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [0, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 2, [Yes, Yes, Yes], Yes, 4], [2, 1, 3, [Yes, Yes, No], No, 6], [3, 2, 2, [Yes, Yes, No], No, 4]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0083/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 84. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 3], [2, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 4]], objective=[1, 2], direction=max. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

View answer and explanation([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [1, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 0, [Yes, Yes, Yes], Yes, 1], [2, 2, 2, [Yes, Yes, Yes], Yes, 6], [3, 2, 3, [Yes, Yes, No], No, 8]], 6, [2])

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [1, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 0, [Yes, Yes, Yes], Yes, 1], [2, 2, 2, [Yes, Yes, Yes], Yes, 6], [3, 2, 3, [Yes, Yes, No], No, 8]], 6, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0084/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 85. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 4], [3, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 5]], objective=[2, 2], direction=min. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

View answer and explanation([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [2, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 1, [Yes, Yes, Yes], Yes, 4], [2, 2, 4, [Yes, Yes, No], No, 12], [3, 3, 2, [Yes, Yes, Yes], Yes, 10]], 0, [0])

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [2, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 1, [Yes, Yes, Yes], Yes, 4], [2, 2, 4, [Yes, Yes, No], No, 12], [3, 3, 2, [Yes, Yes, Yes], Yes, 10]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0085/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 86. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 0], [4, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 6]], objective=[-2, 2], direction=max. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [-2, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 2, [Yes, Yes, Yes], Yes, 2], [2, 2, 0, [Yes, Yes, Yes], Yes, -4], [3, 4, 2, [Yes, Yes, Yes], Yes, -4]], 2, [1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0086/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 87. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 1], [5, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 7]], objective=[-1, 2], direction=min. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [-1, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 3, [Yes, Yes, Yes], Yes, 5], [2, 2, 1, [Yes, Yes, Yes], Yes, 0], [3, 5, 2, [Yes, Yes, Yes], Yes, -1]], -1, [3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0087/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 88. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 2], [0, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 8]], objective=[0, 2], direction=max. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [0, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 0, 2, [Yes, Yes, Yes], Yes, 4], [2, 1, 0, [Yes, Yes, Yes], Yes, 0], [3, 2, 2, [Yes, Yes, Yes], Yes, 4]], 4, [1, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0088/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 89. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 3], [1, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 9]], objective=[1, 2], direction=min. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

View answer and explanation([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [1, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 1, [Yes, Yes, Yes], Yes, 3], [2, 1, 2, [Yes, Yes, Yes], Yes, 5], [3, 2, 3, [Yes, Yes, Yes], Yes, 8]], 0, [0])

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [1, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 1, [Yes, Yes, Yes], Yes, 3], [2, 1, 2, [Yes, Yes, Yes], Yes, 5], [3, 2, 3, [Yes, Yes, Yes], Yes, 8]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0089/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 90. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 4], [2, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 3]], objective=[2, 2], direction=max. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

View answer and explanation([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [2, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 2, [Yes, Yes, Yes], Yes, 6], [2, 2, 2, [Yes, Yes, No], No, 8], [3, 2, 4, [Yes, Yes, No], No, 12]], 6, [1])

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [2, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 2, [Yes, Yes, Yes], Yes, 6], [2, 2, 2, [Yes, Yes, No], No, 8], [3, 2, 4, [Yes, Yes, No], No, 12]], 6, [1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0090/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 91. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 0], [3, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 4]], objective=[-2, 2], direction=min. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [-2, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 3, [Yes, Yes, Yes], Yes, 4], [2, 2, 0, [Yes, Yes, Yes], Yes, -4], [3, 3, 2, [Yes, Yes, No], No, -2]], -4, [2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0091/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 92. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 1], [4, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 5]], objective=[-1, 2], direction=max. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [-1, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 0, [Yes, Yes, Yes], Yes, -1], [2, 2, 1, [Yes, Yes, Yes], Yes, 0], [3, 4, 2, [Yes, Yes, No], No, 0]], 0, [0, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0092/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 93. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 2], [5, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 6]], objective=[0, 2], direction=min. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [0, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 1, [Yes, Yes, Yes], Yes, 2], [2, 2, 2, [Yes, Yes, Yes], Yes, 4], [3, 5, 2, [Yes, Yes, No], No, 4]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0093/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 94. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 3], [0, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 7]], objective=[1, 2], direction=max. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

View answer and explanation([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [1, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 0, 2, [Yes, Yes, Yes], Yes, 4], [2, 1, 2, [Yes, Yes, Yes], Yes, 5], [3, 2, 3, [Yes, Yes, Yes], Yes, 8]], 8, [3])

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 7]], [1, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 0, 2, [Yes, Yes, Yes], Yes, 4], [2, 1, 2, [Yes, Yes, Yes], Yes, 5], [3, 2, 3, [Yes, Yes, Yes], Yes, 8]], 8, [3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0094/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 95. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 4], [1, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 8]], objective=[2, 2], direction=min. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 8]], [2, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 2, [Yes, Yes, Yes], Yes, 6], [2, 1, 3, [Yes, Yes, Yes], Yes, 8], [3, 2, 4, [Yes, Yes, Yes], Yes, 12]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0095/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 96. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 0], [2, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 9]], objective=[-2, 2], direction=max. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 9]], [-2, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 0, [Yes, Yes, Yes], Yes, -2], [2, 2, 0, [Yes, Yes, Yes], Yes, -4], [3, 2, 2, [Yes, Yes, Yes], Yes, 0]], 0, [0, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0096/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 97. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 1], [2, 1], [3, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 3]], objective=[-1, 2], direction=min. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 3]], [-1, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 1, [Yes, Yes, Yes], Yes, 1], [2, 2, 1, [Yes, Yes, Yes], Yes, 0], [3, 3, 2, [Yes, Yes, No], No, 1]], 0, [0, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0097/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 98. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 2], [2, 2], [4, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 4]], objective=[0, 2], direction=max. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 4]], [0, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 2, [Yes, Yes, Yes], Yes, 4], [2, 2, 2, [Yes, Yes, Yes], Yes, 4], [3, 4, 2, [Yes, Yes, No], No, 4]], 4, [1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0098/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 99. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 3], [2, 3], [5, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 5]], objective=[1, 2], direction=min. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

View answer and explanation([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [1, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 3, [Yes, Yes, Yes], Yes, 7], [2, 2, 3, [Yes, Yes, Yes], Yes, 8], [3, 5, 2, [Yes, Yes, No], No, 9]], 0, [0])

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 5]], [1, 2], min, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 1, 3, [Yes, Yes, Yes], Yes, 7], [2, 2, 3, [Yes, Yes, Yes], Yes, 8], [3, 5, 2, [Yes, Yes, No], No, 9]], 0, [0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0099/)

Linear programming · qf-app21-lp-finite-optimum · candidate





## 100. All Tied Optimizers among the Explicit Feasible Candidates

Use the complete explicitly supplied finite candidate grid, integer constraints A*x+B*y≤c and linear objective u*x+v*y. Feasibility precedes objective comparison; an optimum among these candidates is not a general continuous-domain LP optimum or dual certificate. points=[[0, 0], [1, 0], [2, 4], [0, 2]], constraints=[[-1, 0, 0], [0, -1, 0], [1, 1, 6]], objective=[2, 2], direction=max. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. At least one canonical candidate must be feasible. Give (canonical constraints,objective,direction,every [index,x,y,constraint truth list,feasible?,objective value] row,best feasible value,all tied optimal canonical indices).

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

Compare only feasible rows, preserve all ties and restrict the optimality claim to the supplied finite grid. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is ([[-1, 0, 0], [0, -1, 0], [1, 1, 6]], [2, 2], max, [[0, 0, 0, [Yes, Yes, Yes], Yes, 0], [1, 0, 2, [Yes, Yes, Yes], Yes, 4], [2, 1, 0, [Yes, Yes, Yes], Yes, 2], [3, 2, 4, [Yes, Yes, Yes], Yes, 12]], 12, [3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r06-linear-programming-0100/)

Linear programming · qf-app21-lp-finite-optimum · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261021-r06-linear-programming-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261013-advance-20261021-r06-linear-programming-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261021-r06-linear-programming-foundations/validation-report.json)