1. 3-3 Optimization with Linear Programming
Find the maximum and minimum values of a function over a region.
Solve real-world problems.

2. Linear programming is a method for finding maximum or minimum (optimum) values of a function over a given system of inequalities.
Each inequality is called a constraint.
The vertices of the solution set define the feasible region.

4. Graph the system of inequalities
Graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region.
(x, y)
12 x + 15 y
f(x, y)