The owner of a baseball team and local stadium has commissioned a study that showed the demand by fans for stadium seats (per playing date) to be P = 22 - 0.2Q, where P is the average price of a ticket and Q represents the number of seats (expressed in thousands). The local stadium seats a maximum of 56,000 per game. The price has been set at $10 per ticket. (Note: Assume that all seats and all games are the same in this problem.)
a. If the owner is only interested in maximizing revenue, has he over-priced or under-priced the tickets?
b. Suppose the owner offers you 10% of any increase in revenues that you can generate. If you can only choose a uniform per-ticket price, what is the maximum amount you can earn per game?