Chapter 2.4, Problem 61E

Minimum average cost. A consulting firm, using statistical methods, provided a veterinary clinic with the cost equation

$\begin{array}{l}C\left(x\right)=0.00048{\left(x-500\right)}^3+60,000\\ \text{ 100}\le x\le \text{1,000}\end{array}$

where $C\left(x\right)$ is the cost in dollars for handling $x$ cases per month. The average cost per case is given by $\bar{C}\left(x\right)=C\left(x\right)/x$

(A) Write the equation for the average cost function $\bar{C}$.

(B) Graph $\bar{C}$ on a graphing calculator.

(C) Use an appropriate command to find the monthly caseload for the minimum average cost per case. What is the minimum average cost per case?