Two-Part Tariff (membership fee for tennis court)

As the owner of a tennis club in a wealty community, you must decide on membership dues and fees for court time. Based on historical data, you understand that there are two types of tennis players in your community. "Serious" players with demand

Q1 = 10 - P

where Q1 is court hours per week, and P is the fee per hour. There are also "occasional" players with demand

Q2 = 8 - 2P

Assume that there are 1000 players of each type, the marginal cost of court time is zero. You have fixed costs of $10,000 per week.

(1) Suppose you want set a membership fee to allow both type of players to play, what should be the membership fee per week? What is your profit per week?

(2) After reviewing historical data, you have realized that it is feasible to set different membership fees for each type of player. For example, the occasional players play no more than 8 hours per week, so you have decided to charge a higher fee for those who play more than 8 hours per week. What is the weekly fee you should charge each group? What is your profit per week?