A firm's total cost of producing Q units of output is C(Q)= 500+20Q. There are ten potential consumers of the firm's product: six "rich" consumers, each with inverse demand P(Q)= 100-5Q; and four "poor" consumers, each with inverse demand P(Q)= 100-80Q.

(a) What is the largest fixed fee (F_poor) that a poor consumer would pay for the right to purchase the product at a per-unit price equal to marginal cost? What is the corresponding largest fixed fee (F_rich) that a rich consumer would pay?

(b) Suppose a two-part tariff is implemented. The per-unit price is set equal to the firm's marginal cost, and the fixed fee is set equal to F_{poor .} How much profit would the firm earn if it operated under this tariff?