Question

In a circus, an average of 500 people pay $15 each to attend a performance. For each $2 increase in ticket price, the number of ticket buyers will decrease by 40. Find the number of dollars the price must be increased to achieve maximum revenue.

Answer 1

Problem

In a circus, an average of 500 people pay $15 each to attend a performance. For each $2 increase in ticket price, the number of ticket buyers will decrease by 40. Find the number of dollars the price must be increased to achieve maximum revenue.​

Solution

For this case we need to find a function for the attendance and other for the ticket price. and then multiply the two functions:

Price: 15 + 2x

Attendance: 500 -40x

x represent the number of $2 increases

And the revenue would be given by:

R = P* A

R = (15+2x)(500-40x)

R= 7500 - 600x +1000 x -80x^2

R= -80x^2 +400x +7 500

And if we take the derivate of this function we got:

R' = -160 x +400= 0

And solving for x we got:

x= 400/160= 2.5$ would be the increase

And the price would be:

P= 15 +2.5 *2= 20$ per ticket