A clothing company makes coats and slacks. The two resources required are wool cloth and labor. The company has 1600 square yards of wool and 2400 hours of labor available. Each coat requires 5 square yards of wool and 10 hours of labor, whereas each pair of slacks requires 6 square yards of wool and 4 hours of labor. The profit for a coat is $25, and the profit for a pair of slacks is $15. The company wants to determine the number of coats and pairs of slacks to make so that profit will be maximized. (a) Formulate a linear optimization model for this problem by defining the decision variables, objective function and all the constraints. What do they represent? (b) Find the optimal solution of this model by hand by graphing the feasible region and determining all corner points.