Question

A toy company has determined that the revenue generated by a particular toy is modeled by the following equation: 13x - 0.025x² 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?

Answer 1

R(x) = 13x - 0.025x^2
For maximum R, R'(x) = 0
R'(x) = 13 - 0.05x = 0
0.05x = 13
x = 13/0.05 = 260

R(260) = 13(260) - 0.025(260)^2 = 3380 - 1690 = 1690
Maximum revenue = $1,690,000

Answer 2

When taking the quiz, make sure to enter 1690 as your answer and not 1,690,000 or else it will be considered wrong due to the fact that the question asks for the number in units of thousands. (: