Question

The total revenue for Sarah's Vacation rentals is given as the function R(x) = 100x-0.25x^2 , where x is the number of villas rented .what number if villas rented produces the maximum revenue?____ villas

Answer 1

To calculate the maximum value of the function, let's calculate the first derivative and equal it to zero, as following:

$\begin{gathered} \frac{dR}{dx}=100-0.50x \\ \\ \Rightarrow100-0.50x=0 \end{gathered}$

Solving for x :

$\begin{gathered} 100-0.5x=0\rightarrow100=0.5x\rightarrow\frac{100}{0.5}=x \\ \Rightarrow x=200 \end{gathered}$

Therefore, we can say that 200 rented villas produce the maximum revenue