Average Costs $\bar { C } ( x ) = 7 x + \frac { 1372 } { x } , \quad x > 0$

Multiple Choice

Average costs. Suppose the average costs of a mining operation depend on the number of machines used, and average costs, in dollars, are given by $\bar { C } ( x ) = 7 x + \frac { 1372 } { x } , \quad x > 0$ , where x is the number of machines used. How many machines give minimum average costs?

A) Using 14 machines gives the minimum average costs.
B) Using zero machines gives the minimum average costs.
C) Using 24 machines gives the minimum average costs.
D) Using 28 machines gives the minimum average costs.
E) Using 33 machines gives the minimum average costs.