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Rogers Place can hold a maximum number of 18,500 fans for an Edmonton Oilers hockey game....

Rogers Place can hold a maximum number of 18,500 fans for an Edmonton Oilers hockey game. Based on historical data, at an average ticket price of $200, an average of 16,000 fans buy a ticket and attend the game. For each $5 that the average ticket price is increased (or lowered), 500 fans less (or more) buy a ticket.

(a) Let x(p) be the number of fans attending a game at an average price p. Determine the function x(p).

(b) What is the average ticket price at which the revenues are maximized?

(c) Because of the Oilers’ strong start this season, the demand for tickets to Oilers hockey games has risen. At an average ticket price of $200, an average of 18,000 fans buy a ticket and attend the game this season. We still have that for each $5 the average ticket price is increased (or lowered), 500 fans less (or more) buy a ticket. Using this information, what is now the average ticket price at which the revenues are maximized?

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