Question

A baseball team plays in a stadium that holds 52,000 spectators. With the ticket price at...

A baseball team plays in a stadium that holds 52,000 spectators. With the ticket price at $10, the average attendance at recent games has been 33,000. A market survey indicates that for every dollar the ticket price is increased, the attendance decreases by 3,000.

(a) Let x be the ticket price (in dollars). Find q(x) which represents how many people will attend the ballgame when the ticket price is x.

(b) The ballpark’s revenue is R(x) = x · q(x). Find this quadratic function.

(c) Determine what price the ballpark should charge for a ticket in order to maximize revenue.

(d) What is the maximum revenue the ballpark can generate?

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