# Question 25047: Qualify Dimensions and the Fixed Convention without Claiming Feasibility

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This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0049-25047 · q-20261015-advance-20261114-r06-linear-program-standard-form-0022



## Original question and givens

Use the one fixed convention maximize c^T*x, subject to A*x≤b and x≥0, with A=[[22, 1], [-1, 23]], b=[46, 23], c=[24, -22]. 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=[[22, 1], [-1, 23]], b=[46, 23], c=[24, -22]. 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](https://ocme.evemisslab.com/en/mko/mko-linear-program-standard-form/)





## Step-by-step derivation

S001 · impliesBefore

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

After

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

Conditions: none

List the full source field order without JavaScript.LP boundary modes all have6 fields but select different roles from the original mode,not answer shape.

Step identifiers and dependenciesRule: source_ordered_fields_without_JS · Uses: G001





S002 · impliesBefore

source roles = [[[22, 1], [-1, 23]], [46, 23], [24, -22]]

After

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

Conditions: none

Check rectangular rows and b/c dimensions.This is one declared standard-form convention,not the only textbook convention.A,b,c may have either sign;qualified dimensions do not prove feasibility.

Step identifiers and dependenciesRule: LP_fixed_max_le_nonnegative_signature_NOT_feasibility · Uses: G001, S001









## 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, [[22, 1], [-1, 23]], [46, 23], [24, -22], 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.

Source hashes and review receipts
- input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
- original question SHA-256: cf58e136235b40c7445e67decef72afd6f0e74065ed09962f83f9cd54297cb8d
- candidate record SHA-256: 154492cf5e4b0e155be8083da2c58280331de4fab988b2cda355dce9462eea9c
- semantic review receipt SHA-256: 6212b8b0b3b273f3a514e26ebd17d7e81219c56a8f47e40047ee2b6bf01d1ba3
- question-first witness SHA-256: f32a23d5e1b66c7794c60def58741bcdfacff24f3cdfc9bc48109c8f71543cf3
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261114-r06-linear-program-standard-form-0022.json)