A monopolist sells two competitive products, A and B, for which the demand equations are PA = 80 - 2.5x and pg = 125 - 10y, where pA and pg are the unit prices (in $) of A and B respectively, and x and y represent the quantity demanded of product A and B respectively. The joint-cost function (in S) is C(x, y) = 200 + 5(x + y) a. Determine the joint-profit function in dollar, P(x, y) b. How many units of A and B should be sold to obtain a relative maximum profit for the monopolist? (Use the second-derivative test to justify your answer.) c. Determine the maximum profit. T d. Determine the selling prices of both products A and B to realize the relative maximum profit