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 :

3

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, $MC=\frac{d}{dx}(27+15x+3x^2)$

$=15+6x$

$AC=MC$

$\frac{27}{x}+15+3x=15+6x$

$⇒\frac{27}{x}=6x-3x$

$⇒x^2=9⇒x=3$