Question

A publishing company expects to sell 5000 copies of a new book from its web site, if the company charges $30 per book. The company expects that 500 more books would be sold for each price reduction of $2. What price would maximize the company's revenue?

Answer 1

Let the revenue be = R

Therefore, R = price x quantity

R = (30 - 2x) ( 5000 + 500x)

=
`150000 + 5000x - 1000x^2`

For the maximum revenue,

`$(dR)/(dx) = 0$`

`$-2000x+5000=0$`

`$x=2.5$`

`$(d^2R)/(dx^2)=-2000<0$`

At
`x=2.5`, the revenue is maximum.

So the price for the maximum company revenue =
`$30-2x$`

`$=30-2(2.5)$`

= 30 - 5

= 25

Therefore, the price that will maximize the company's revenue is $25.