Chapter 4, Problem 59RE

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# A hockey team plays in an arena with a seating capacity of 15,000 spectators. With the ticket price set at $12, average attendance at a game has been 11,000. A market survey indicates that for each dollar the ticket price is lowered, average attendance will increase by 1000. How should the owners of the team set the ticket price to maximize their revenue from ticket sales? To determine To Set: the ticket price to maximize the revenue from ticket sales. Explanation Given: The seating capacity of the arena is 15,000 and initial price of the ticket is$12.

The average attendance was 11000.

Calculation:

Survey suggests that for a dollar decrease in ticket rate the increase in the attendance will be by 1000.

Let x be the decrease in the price of the rate of ticket.

Hence, the new rate of ticket is 12x .

As per the survey the average attendance for new rate will be 11000+1000x

Revenue generated is given by R(x)=(12x)(11000+1000x) .

Maximize R(x) in order to maximize revenue

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