Linear Programming

This lesson is very similar to the previous one about solving and graphing systems of inequalities. However, this section is more focused on word problems that apply the shaded graphs to everyday life. The problems often ask for the maximum amount or minimum amount of something, so you have to find the vertices of the shaded region, as the best answer always lies at one of these. Here are the steps:

1. Read the problem carefully.
2. Write the constraints or inequalities.
3. Graph the inequalities. Find the feasible region.
4. Find the vertices of the feasible region.
5. Write a function to find the minimum or maximum value. (This format: z = ax + by).
6. Plug the vertices into the function.
7. Find the maximum or minimum.

Many of these problems involve maximizing profit or minimizing costs for a company. Because of this, the variables x and y often correspond to certain commodities, and the a and b in the above equation (in step 5) are usually either the cost of each commodity or the profit gained from selling each commodity.