For the following exercises, solve using the graphical method. Choose your variables, write the objective function and the constraints, graph the constraints, shade the feasibility region, label all corner points, and determine the solution that optimizes the objective function.
A department store sells two types of televisions: Regular and Big Screen. The store can sell up to 90 sets a month. A Regular television requires 6 cubic feet of storage space, and a Big Screen television requires 18 cubic feet of space, and a maximum of 1080 cubic feet of storage space is available. The Regular and Big Screen televisions take up, respectively, 2 and 3 sales hours of labor, and a maximum of 198 hours of labor is available. If the profit made from each of these types is $60 and $80, respectively, how many of each type of television should be sold to maximize profit, and what is the maximum profit?