Summary

To solve a linear programming problem (two variables)

1. Graph the region corresponding to the system of constaints. This region contains the feasible solutions.

2. Find the vertices (corners) of the feasible region.

3. Evaluate the objective function at each vertex.

If the region is bounded , the largest and smallest values obtained correspond to the maximum and minimum. If the region is unbounded , the optimal value you are looking for will be one of these values.