The cost of manufacturing x units of a commodity is $27+15x+3x^2$. Then the value of output (x) when average cost is equal to Marginal cost is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3
The cost function is,
$C(x)=27+15x+3x^2$
Average cost, $AC=\frac{C(x)}{x}=\frac{27}{x}+15+3x$
Marginal cost, $MC=\frac{d}{dx}(27+15x+3x^2)$
$=15+6x$
$AC=MC$
$\frac{27}{x}+15+3x=15+6x$
$⇒\frac{27}{x}=6x-3x$
$⇒x^2=9⇒x=3$