Question

The total revenue for Fred's Estates LLC is given as the function R(x) = 100x - 0.4x2, where x is the number of roomsrented. What number of rooms rented produces the maximum revenue?

Answer 1

The maximum revenue will be at the x-coordinate of the vertex point of the equation

`R(x)=100x-0.4x^2`

The form of the quadratic function is

`f(x)=ax^2+bx+c`

Its vertex is (h, k), where

`h=-(b)/(2a)`

From the given function

`\begin{gathered} a=-0.4 \\ b=100 \end{gathered}`

Substitute them to find the value of h

`\begin{gathered} h=-(100)/(-0.4) \\ h=250 \end{gathered}`

Then the x-coordinate of the maximum point of the function is 250

The number of rooms rented which produces the maximum revenue is 250 rooms

The answer is 250