Science:Math Exam Resources/Courses/MATH100 C/December 2024/Question 11 (c)/Solution 1

Since $f(p)$ is a parabola pointing down, its maximum occurs at its only critical point. To find the critical point, we compute the derivative:

$$f^{\prime }(p)=-p+135.$$

Setting it to zero, we get $-p+135=0,\text{and}p=135.$

So, they should charge $135 per night.