Question 25027: Qualify Dimensions and the Fixed Convention without Claiming Feasibility

Original question and givens

Use the one fixed convention maximize c^T*x, subject to A*x≤b and x≥0, with A=[[2, 1], [-1, 3]], b=[6, 3], c=[4, -2]. Require a nonempty rectangular exact rational matrix and matching vectors. Coefficients and b may have either sign; variable nonnegativity is a constraint, not an assumption that every supplied point is feasible. Give (constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate).

• G001 — Use the one fixed convention maximize c^T*x, subject to A*x≤b and x≥0, with A=[[2, 1], [-1, 3]], b=[6, 3], c=[4, -2]. Require a nonempty rectangular exact rational matrix and matching vectors. Coefficients and b may have either sign; variable nonnegativity is a constraint, not an assumption that every supplied point is feasible. Give (constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-linear-program-standard-form

Step-by-step derivation

source roles = [lp-standard-dimension-sign-qualification]

derived = [[constraint_count, variable_count, A, b, c, convention, dimensions_qualified, certificate]]

source roles = [[[2, 1], [-1, 3]], [6, 3], [4, -2]]

derived = [2, 2, maximize cTx subject Ax<=b,x>=0, Yes]

Reverse checks

• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(2, 2, [[2, 1], [-1, 3]], [6, 3], [4, -2], maximize_cTx_subject_to_Ax_less_equal_b_and_x_nonnegative, Yes, one_fixed_standard_form_convention)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.