Chapter 3.R, Problem 47E

### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Chapter
Section

### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
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 find: The ticket price to maximize the revenue from ticket sales Explanation 1) Concept: a) The function has local minima when f'x<0, and has local maxima when f'x>0 b) The function is maximum when f"(x)<0 minimum when f"(x)>0 2) Given: a) Seating capacity of spectators is 15000 b) Ticket price is set at$12

c) Average attendance at a game has been 11000.

d) Also for each dollar the ticket price is lowered, the average attendance increases by 1000.

3) Calculation:

Let x be the decrease in price. Then, the price of the ticket will be 12-x, and the average attendance will be 11000+1000x

Therefore, the revenue per game will be equal to the ticket price multiplied by the attendance.

Rx=12-x·11000+1000x

Rx=-1000x2+1000x+132000 for 0x4

The maximum increase in attendance is 4000

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