The demand for a certain product is represented by the function $p = 300 +25x-x^2$ (in rupees), where $x$ is the number of units demanded and $p$ is the price per unit, then the marginal revenue when 15 units are sold,is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ₹375 **
The price function is $p = 300 + 25x - x^{2}$.
Revenue: $R = px = x(300 + 25x - x^{2})$
$R = 300x + 25x^{2} - x^{3}$
Marginal revenue: $R' = \frac{dR}{dx} = 300 + 50x - 3x^{2}$
At $x = 15$:
$R'(15) = 300 + 50(15) - 3(15^{2})$
$= 300 + 750 - 3(225)$
$= 1050 - 675$
$= 375$
The marginal revenue when 15 units are sold is ₹375.