A company manufactures two types of trucks. Each truck must go through the painting shop and the assembly shop. If the painting shop were completely devoted to painting type 1 trucks, 800 per day could be painted, whereas if the painting shop were completely devoted to painting type 2 trucks, 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, 1500 per day could be assembled, whereas if the assembly shop were completely devoted to assembling truck 2 engines, 1200 per day could be assembled. It is possible, however, to paint both types of trucks in the painting shop. Similarly, it is possible to assemble both types in the assembly shop. Each type 1 truck contributes $1000 to profit; each type 2 truck contributes $1500. Perform the tasks below to formulate this problem and solve it by hand to maximize the company's profit. (Hint: One approach, but not the only approach, is to try a graphical procedure first and then deduce the constraints from the graph.)

(a) Define your decision variables clearly

(b) Write down the objective

(c) Write down the constraints

(d) Graphically solve the problem