A firm sells $x$ units at ₹$(60 - 2x)$ each, and making them costs ₹$(12x + 50)$. How many units give the largest profit?

Explanation

1. 01

   Profit $P = (60 - 2x)x - (12x + 50) = 48x - 2x^{2} - 50$.

2. 02

   $P' = 48 - 4x = 0$ at $x = 12$, and $P'' = -4 < 0$: a maximum.