LaTeX
\min_x c^Tx\quad\text{s.t.}\quad Ax=b,\;x\geq0Variables
- c: objective coefficients
- A: constraint matrix
- b: right-hand side
- x: decision vector
How to use this formula
Expresses a linear objective with equality constraints and nonnegative variables.
Important notes
- Other linear programs can be transformed into this form.
- Feasibility and boundedness must be checked.
Quick example
Slack variables convert many inequalities into equalities.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Other linear programs can be transformed into this form.
- Specify the objective, constraints, feasible domain, and any convexity or differentiability assumptions used to justify the result.
Worked example
Slack variables convert many inequalities into equalities.
Common mistakes
- Before substituting values into Linear Program Standard Form, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- Do not treat a stationary point as a global optimum without checking constraints, boundaries, and the required optimality conditions.
Continue the workflow
Use Linear Program Standard Form in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\min_x c^Tx\quad\text{s.t.}\quad Ax=b,\;x\geq0. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Linear Program Standard Form used for?
Expresses a linear objective with equality constraints and nonnegative variables.
Can I copy this formula as LaTeX?
Yes. Copy \min_x c^Tx\quad\text{s.t.}\quad Ax=b,\;x\geq0 or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.