A baseball team's attendance depends on the number of games it wins per season and on the price of its tickets. The demand function it faces is Q = N(20 - p), where Q is the number of tickets (in hundred thousands) sold per year, p is the price per ticket, and N is the fraction of its games that the team wins. The team can increase the number of games it wins by hiring better players. If the team spends C million dollars on players, it will win .7 - 1/C of its games. Over the relevant range, the marginal cost of selling an extra ticket is zero.
a. Write an expression for the firm's profits as a function of ticket price and expenditure on players.
b. Find the ticket price that maximizes revenue.
c. Find the profit-maximizing expenditure on players and the profit-maximizing fraction of games to win.