The cost of making $x$ units is $C(x) = x^{2} + 2x + 400$ rupees. At what output is the average cost per unit least?

Explanation

1. 01

   Average cost $AC = x + 2 + \frac{400}{x}$, so $AC' = 1 - \frac{400}{x^{2}}$.

2. 02

   $AC' = 0$ at $x = 20$, and $AC'' = \frac{800}{x^{3}} > 0$: the least average cost, ₹42 a unit.