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*2x=0`

=
`10-0.5x=0`

`x=(10)/(0.05)`

x= 200

Hence, r(200) =
`10*200-0.025*200^(2)`

Solving it we get,

r(200) = 1000

Hence, maximum revenue is $1000.