Question

A toy company has determined that the revenue generated by a particular toy is modeled by the following equation: 10x - 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

Answer:

Maximum revenue = 1000 thousands of dollars.

Explanation:

We have the revenue equation $r(x)=10x - 0.025x^2$, where x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars.

At maximum revenue the derivative of equation is zero

So, $r'(x)=0\\ \\10 - 0.025*2x=0\\ \\ x=10/0.05\\ \\ x=1000/5=200$

So maximum revenue is when 200 thousands of toys are produced.

Maximum revenue, $r(200)=10*200 - 0.025*200^2\\ \\ r(200)=1000$

Maximum revenue = 1000 thousands of dollars.