Consider a firm that manufactures a product A at cost CA, and faces a single period random demand D with density function f(D) and CDF F(D) for the product. The firm sells the product for price pi > CA per unit, and if the firm runs out of product demand is lost. If the firm has extra product, the product is disposed of at no additional cost. The firm can also (or in addition) produce another version of the product B at cost CB > CA to meet the same demand at the same price pi. The advantage of this product is that the firm has entered into an agreement with an overseas distributor such that the distributor is willing to pay the firm p2, p1>p2> ca per unit for up to K units of the product that the firm might have left over at the end of the selling period. (a) Without any computation, can you find out the optimal amount of product B the firm should manufacture? Briefly explain why. (b) Write a mathematical expression for the firm's total expected profit.