When the price is ₹$(100 - x)$ per unit, a shop sells $x$ units. How many units give the largest revenue?

Explanation

1. 01

   Revenue $R(x) = x(100 - x) = 100x - x^2$.

2. 02

   $R'(x) = 100 - 2x = 0$ at $x = 50$, and $R'' < 0$: a maximum.