Question

The cost function of a firm $C\left(x\right)=4x^2-x+70$. Find the average cost when $x=3$.

• A. $\frac{104}{3}$
• B. $\frac{103}{3}$
• C. $\frac{105}{3}$
• D. $\frac{103}{4}$

Answer 1

Answer: (B)

$\frac{103}{3}$

$\Rightarrow$ We have, $C\left(x\right)=4x^2-x+70$.

$\Rightarrow$ Average cost = $\frac{C\left(x\right)}{x}$

$\Rightarrow$ Average cost = $\frac{4x^2-x+70}{x}$

$\Rightarrow$ Average cost = $4x-1+\frac{70}{x}$

$\Rightarrow$ Substitute value of $x=3$.

$\Rightarrow$ Average cost = $12-1+\frac{70}{3}=\frac{36-3+70}{3}=\frac{103}{3}$

$\therefore$ $Averagecost=\frac{103}{3}$