A monopolist firm faces demand from two groups. Group A has demand QA = 100 - 8pA and thus MR = (1/8)*(100 - 2QA). Group B has demand and QB = 100 - 4pB and thus MR = (1/4)*(100 - 2QB). The monopolist has a cost function C(Q) = 2QA + 2QB and marginal cost MC = 2. The equation for marginal revenue from a combined demand curve is MR = 50/3 - Q/6. a. If the firm can not price discriminate, what is the optimal (from the firm's perspective) price and quantity? How much profit does the firm make? b. If they are allowed to price discriminate, what are the optimal prices and quantities for each group? How much profit does the firm make?