Suppose there is a firm that produces a good that has a constant marginal cost of $5 per unit. The firm faces a market demand curve given by P = 50 - Q, where P is the price of the good and Q is the quantity of the good.

a) Derive the firm's marginal revenue curve.

b) Derive the firm's average total cost curve.

c) Determine the profit-maximizing output level and price for the firm.

d) Calculate the firm's profit at the profit-maximizing output level.