For a manufacturer, total cost function is given by $c=\frac{x^2}{25}+2x.$ Which of the following are correct ?
A. 2.6 is the marginal cost when 5 units are produces.
B. $\frac{2x}{25}+2 $ is the average cost function.
C. $\frac{x}{25}+2 $ is the average cost function.
D. 2.4 is the marginal cost when 5 units are produced.
E. $\frac{x}{25}+1 $ is the average cost function.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
Given total cost
$C=\frac{x^2}{25}+2x$
Marginal cost
$MC=\frac{dC}{dx}$
$MC=\frac{2x}{25}+2$
At $x=5$
$MC=\frac{2(5)}{25}+2$
$=\frac{10}{25}+2$
$=0.4+2=2.4$
So statement (D) is correct and (A) is incorrect.
Average cost
$AC=\frac{C}{x}$
$AC=\frac{\frac{x^2}{25}+2x}{x}$
$AC=\frac{x}{25}+2$
So statement (C) is correct.
The correct statements are (C) and (D).