Solving a System of Linear Equations in Two Variables - Problem 15

Linear programming is the name for maximizing or minimizing some objective function, often involving cost or profit. Start by writing your objective function, which will help you define the variables that will be on your axes. Next, you will write constraints with inequality signs for each constraint in the problem scenario, and graph them with shading on an x-y plane. The darkened shaded region is called the feasible region, and the maximum (or minimum) of an objective function will always occur at a vertex of the feasible region. Find the vertices using systems of equations, and then evaluate the objective function at each vertex. Select the highest (or lowest) combination.