Question

The manufacturer of a CD player has found that the revenue R (in dollars) is R(p) = -5p2 + 1510p, when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar?

Answer 1

maximum revenue is 114005

Explanation:

for the function R(p) to attain its maximum value R'(p) must be 0.

that is the slope of R(p) must be 0.

R(p) =
`-5p^(2) + 1510p`

R'(p) =
`-10p + 1510`

therefore
`-10p + 1510 = 0`

therefore R(p) is maximum when p = 151

therefore R(151) =
`-5(151^(2) )+1510(151)`

= 114005