Consider a team with a stadium that has a seating capacity of Q = 50 , where Q is measured in thousands of fans. Demand for tickets is given by P =100Q , where P is the pergame price of a ticket and Q is the number of fans attending per game. For simplicity, assume that the marginal cost per fan is constant at 20 and fixed costs are 600 (in thousands of dollars) per game.

Now assume that the team can separate fans into two groups, such that demand among hardcore fans is P1 =132 2Q1 and demand among fairweather fans is P2 = 280.5Q2

a) Calculate the profit-maximising prices, P1 * and P2 * , quantities, Q1 * and Q2 * , and maximum profit, * .