Question

The total revenue for dante's villas is given as the function r(x)=300x−0.2x2, where x is the number of rooms filled. What number of rooms filled produces the maximum revenue?

Answer 1

Solution:- Given that the total revenue function

$r(x)=300x-0.2x^2$ ,where x is the number of rooms filled

Now, differentiating the function w.r.t. x,we get

$r'(x)=300-0.4x$

To find critical points ,Put $r'(x)=0$

$\Rightarrow300-0.4x=0\\\Rightarrow0.4x=300\\\Rightarrow x=750\\\text{Now}\\r"(x)=-0.4$