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The cost of manufacturing x units of a commodity is $27 + 15x+3x^2$. Find the output where AC = MC. |
$x=1$ $x=2$ $x=3$ $x=4$ |
$x=3$ |
The correct answer is Option (3) → $x=3$ $C(x)=27 + 15x+3x^2$ $∴AC=\frac{C}{x}=\frac{27}{x}+15+3x$ $MC=\frac{dC}{dx}=\frac{d}{dx}(27 + 15x+3x^2)=15+6x$ $∴MC=AC⇒15+6x=\frac{27}{x}+15+3x⇒3x=\frac{27}{x}$ $⇒x^2=9⇒x=3$ |
