#### Problem 31E

31. If $p(x)$ is the total value of the production when there are $x$ workers in a plant, then the average productivity of the workforce at the plant is

$$A(x)=\frac{p(x)}{x}$$

(a) Find $A^{\prime}(x)$. Why does the company want to hire more workers if $A^{\prime}(x)>0 ?$

(b) Show that $A^{\prime}(x)>0$ if $p^{\prime}(x)$ is greater than the average productivity.