The owner of a baseball team and local stadium has commissioned a study that sho

Question

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. Suppose the owner offers you 10% of the revenues. If you can only choose a uniform per-ticket price, what is the maximum amount you can earn per game? ( Assume that all seats and all games are the same in this problem.)

Explanation / Answer

P=22-0.2q

total revenue=P*q

TR=22q-0.2q2

differentiating bot sides and equating it to 0 we get,

22-0.4q=0

q=55

when q=55

p=22-.2(55)=11

maximum revenue per game=11*55000=605,000

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