The demand for a certain product is represented by the function $p = 200 + 20x - x^2$ (in ₹) where x is the number of units demanded and p is the price per unit. Find the marginal revenue and obtain the marginal revenue when 10 units are sold, and interpret it.

$MR=200+40x−x^2; MR(10)=300$

The correct answer is Option (4) → $MR=200+40x−x^2; MR(10)=300$

Given $p = 200 + 20x - x^2$

∴ Total revenue $R = px = 200x + 20x^2-x^3$

$MR = \frac{dR}{dx}= 200 + 40x - 3x^2$.

$\left.MR\right|_{x = 10} = 200 + 40 × 10 − 3 × 10^2 = 300$

This means that when sales are increased from 10 to 11 units, additional revenue obtained is ₹300.