Linear programming

Math

Definition

A method of finding the maximum or minimum value of a linear objective function subject to a set of linear inequality constraints. Solutions occur at the vertices (corner points) of the feasible region.

How It Works

  1. Define the variables and write the objective function to maximize or minimize.
  2. Write the constraint inequalities.
  3. Graph the constraints to find the feasible region.
  4. Identify the vertices (corner points) of the feasible region.
  5. Evaluate the objective function at each vertex.
  6. Select the vertex that gives the optimal (max or min) value.

Examples

  • Maximizing profit when producing two products with limited resources
  • Minimizing cost of a diet that must meet certain nutritional requirements
  • Optimizing shipping routes with capacity constraints

Study This Concept

Practice linear programming with free review games in these units: