only c & d write neatly pls

2. Suppose a monopolist sells to two types of customers: type A and type B. (For simplicity, suppose there is only one type A customer and one type B customer. Type A's inverse demand is described by Pa=200-2Qa. Type B's inverse demand is described by Pb=200-4Qb. The monopolist's marginal cost is zero. a. Suppose the monopolist cannot price discriminate. Find the optimal price, quantity, and profit. b. Suppose the monopolist can engage in 1" degree (perfect) price discrimination. Find the quantities and (bulk) prices for each consumer, and the optimal profit. c. Suppose the monopolist cannot tell which consumer is type A and which is type B, but can charge different prices per unit depending on the number of units purchased. Explain why the pricing strategy used in part (b) will not work in this case. Find the optimal price-quantity combinations to offer and the optimal profit d. Suppose the monopolist can tell which consumer is type A and which is type B, but must charge the same per unit price regardless of the quantity purchased. Find the optimal prices and quantities for type A and type B, and the optimal profit