The cost of manufacturing x units of a commodity is $27 + 15x+3x^2$. Find the output where AC = MC.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $x=3$
$C(x)=27 + 15x+3x^2$
$∴AC=\frac{C}{x}=\frac{27}{x}+15+3x$
$MC=\frac{dC}{dx}=\frac{d}{dx}(27 + 15x+3x^2)=15+6x$
$∴MC=AC⇒15+6x=\frac{27}{x}+15+3x⇒3x=\frac{27}{x}$
$⇒x^2=9⇒x=3$