Question

The total revenue for Joe’s Realty is given as the function R (X) = 200x-0.5x^2, where X is the number of Bella‘s book. What number of villas book produces the maximum revenue?

Answer 1

To find the maximum revenue, we need to derivate the R(x) function and then solve the equation for x:

`R(x)=200x-0.5x^2`

Derivate the function:

`R^(\prime)(x)=200(1)-2(0.5)x=200-1x`

Then:

`200-x=0`

Therefore:

`x=200`

Which x represents the maximum point, now, replace this value on the R(x) function to find the maximum revenue:

`R(x)=200(200)-0.5(200)^2=20000`