The cost of manufacturing units of a commodity is . Find the output for which Average Cost is…

Total Cost: $C(x) = 27 + 12x + 3x^2$. Average Cost: $AC = \frac{C(x)}{x} = \frac{27}{x} + 12 + 3x$. Average Cost is decreasing when $\frac{d(AC)}{dx} < 0$: $\frac{d(AC)}{dx} = -\frac{27}{x^2} + 3 < 0 \implies 3 < \frac{27}{x^2} \implies x^2 < 9$. Since output $x > 0$, Average Cost is decreasing for output $0 < x < 3$ (or $x < 3$ units).