Chapter 2.4, Problem 62E

Minimum average cost. The financial department of a hospital, using statistical methods, arrived at a cost equation

$\begin{array}{l}C\left(x\right)=20x^3-360x^2+2,300x-1,000\\ \text{ 1}\le x\le \text{12}\end{array}$

where $C\left(x\right)$ is the cost in thousands of dollars for handling $x$ thousand 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 to the nearest dollar?