Linear programming
MathDefinition
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
- Define the variables and write the objective function to maximize or minimize.
- Write the constraint inequalities.
- Graph the constraints to find the feasible region.
- Identify the vertices (corner points) of the feasible region.
- Evaluate the objective function at each vertex.
- 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: