# The revenue maximize from ticket sale. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 4, Problem 47RE
To determine

## To find: The revenue maximize from ticket sale.

Expert Solution

The revenue maximize from ticket sale price is $11.50 ### Explanation of Solution Given information: The seating capacity of arena is 15,000 .The ticket prize set$12 ,Average attendance will increase by 1000.
Let X is number of attendance, then the increase in attendance is x11000 ,For each increase of 1000 attendance the price decreased by $1 so for additional attendance, the decrease in price will be 11000×1 And the demand function is, p(x)=1211000(x11000)=23x1000 The revenue function is R(x)=xp(x)=23x21000 Since R(x)=23x500 so R(x)=0 x=11500 This value of X gives an absolute maximum by first derivative test. Then ticket price is, p(x)=2311000(11500)=2311.50=11.50 So the price is$ 11.50 which will maximize the revenue.