Graphical Method for Linear Programming

Steps

1. Graph each constraint (as a line, then shade the appropriate region)
2. Find the feasible region (intersection of all constraint regions)
3. Identify all corner points (vertices) of the feasible region
4. Evaluate the objective function at each corner point
5. The maximum/minimum value is the optimal solution

Example: Solve LP Problem Graphically

Maximize subject to:

Example: Minimization Problem

Minimize subject to:

Corner Point Method Summary

Multiple Optimal Solutions

Example: Multiple Solutions

Maximize subject to: