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) → Rs. 375
The total revenue is price times quantity, and the marginal revenue is its derivative.
\(R = px = x(300 + 25x - x^2)\)
\(R = 300x + 25x^2 - x^3\)
\( \displaystyle MR = \frac{dR}{dx} = 300 + 50x - 3x^2 \)
At \(x = 15\):
\(MR = 300 + 50(15) - 3(15)^2\)
\(= 300 + 750 - 675\)
\(= 375\)
So the marginal revenue is Rs. 375.
CBSE Applied Mathematics (Class XII):
Marginal Cost and Marginal Revenue
