Canonical Finite LP Grids, Feasibility and All Tied Optimizers
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This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.
batch-20261013-advance-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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Linear programming · qf-app21-lp-finite-optimum · candidate
Canonical question JSONL · English JSONL · Validation report