Question

Please help with one 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

The equation is r(x) = 10x - 0.025x² where x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars.

For maximum r, r'(x) = 0

It becomes: r'(x) = $10-0.025\times2x=0$

= $10-0.5x=0$

$x=\frac{10}{0.05}$

x= 200

Hence, r(200) = $10\times200-0.025\times200^{2}$

Solving it we get,

r(200) = 1000

Hence, maximum revenue is $1000.