Your manager receives an updated financial report indicating that Rent-a-Car is losing money, and she wants you to determine a strategy to revive the firm. You both agree that the immediate goal is to maximize economic profit by determining the optimal price for profit maximization. Recall that Rent-a-Car is one of the two rental agencies in town, so you should assume that Rent-a-Car has some market power. You know the following details:

Direct Demand Function: QE = 145.98 - 2.272PownE

Average Variable Cost: AVC = 414.86 - 7.35Q + 0.04Q2

(1) What is the optimal number of contracts that maximize the firm's profit. Explain how you got to this number.

(2) Assuming the firm initiates the optimal number of contracts from (1), what is the price level? What is the marginal cost and average variable cost at the output level?

(3) What is the maximum profit the firm will earn?