2.1 Introduction to Linear Programs

Understanding the fundamental concepts of linear programming and standard form.

Standard Form
Understanding the canonical representation

Basic Structure

A linear program in standard form consists of:

  • Linear objective function to minimize
  • Linear equality constraints
  • Nonnegative variables

Mathematical Form

minimize $c^Tx$ subject to $Ax = b$ and $x \geq 0$
Problem Transformation
Converting to standard form

Common Transformations

  • Inequalities to equalities using slack/surplus variables
  • Free variables to nonnegative variables
  • Maximization to minimization

Examples

See interactive examples of problem transformations in the Standard Form Converter below.

Interactive Learning

Linear Program Visualizer
Visualize linear programming problems and their feasible regions

Objective Function

minimize $1x_1 + 1x_2$

Constraints

Display Options

Standard Form Converter
Learn how to convert linear programs to standard form

Example

Original Form

maximize $2x_1 + 3x_2$
Formula Quiz
Test your understanding of linear programming formulas
Question 1 of 4
What is the standard form of a linear program?