Question

A toy company has determined that the revenue generated by a particular toy is modeled by the following equation:

r(X)=11x-0.025x^2

The variable x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars. What is the maximum revenue the company can earn with this toy?

Give your answer in dollars, without using commas.

Answer 1

r(x) = 11x - 0.025x^2
Revenue is maximum when dr(x)/dx = 0
dr(x)/dx = 11 - 0.05x = 0
0.05x = 11
x = 11/0.05 = 220
The revenue will be maximum when 220000 toys are produced.

r(220) = 11(220) - 0.025(220)^2 = 2,420 - 1,210 = 1,210
Therefore, maximum revenue = $1210000