Work with a partner. Linear programming is a modeling technique that is useful for quantitative decisions in engineering, business, and the sciences. To solve a linear programming problem, you must find the maximum and minimum values of a linear equation within a set of constraints expressed as inequalities. This is called the feasible region, or the solution set of a system of linear inequalities. The extreme values, or maximum and minimum values, of any objective function f (x, y) must occur at the vertices of the feasible region