Suppose that the inverse demand function for a monopolist's product is P (q) = 90 - 0.05q while the firm's total cost function is C (q) = 10 + 20q + 0.15q2. (a) Plot or sketch carefully the demand curve, marginal revenue curve, and marginal cost curve. (b) At what volume of output does marginal revenue equal marginal cost? (c) What are the profit-maximizing output and price? (Note: you should check the second- order condition to verify that your answer is a maximum)