BuyFind

Single Variable Calculus: Concepts...

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

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

Answer to Problem 47RE

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.

Calculation:

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.

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