Linear Program Standard Form Calculator

Standard Form of Linear Program:

\[ \text{Maximize } c^T x \text{ subject to } Ax = b, x \geq 0 \]

Standard Form Representation:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Standard Form in Linear Programming?

The standard form of a linear program is: Maximize cᵀx subject to Ax = b with x ≥ 0. All linear programs can be converted to this form through appropriate transformations of variables and constraints.

2. How the Conversion Works

The calculator performs these conversions:

Minimization → Maximization (multiply objective by -1)
Inequality constraints → Equality (add slack/surplus variables)
Unrestricted variables → Non-negative (split into positive/negative parts)

3. Importance of Standard Form

Details: Standard form is required for many solution algorithms (like simplex method) and makes theoretical analysis of linear programs easier.

4. Using the Calculator

Tips: Enter objective coefficients (c) as comma-separated values. For matrix A, enter each row on a new line with comma-separated values. Enter constraint constants (b) as comma-separated values.

5. Frequently Asked Questions (FAQ)

Q1: Why convert to standard form?
A: Standard form simplifies implementation of solution algorithms and theoretical analysis.

Q2: What about minimization problems?
A: The calculator automatically converts minimize to maximize by negating the objective coefficients.

Q3: How are inequality constraints handled?
A: ≤ constraints add slack variables, ≥ constraints add surplus variables to convert to equalities.

Q4: What if my variables can be negative?
A: Each unrestricted variable is replaced by two non-negative variables (x = x⁺ - x⁻).

Q5: Is standard form unique?
A: No, there can be multiple equivalent standard forms for the same problem.