The demand for a certain product is represented by the function \(p = 150+10x - x^2\) (in Rs.) where \(x\) is the number of units demanded and \(p\) is the price per unit, then the value of marginal revenue, when 10 units are sold, is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs.50
The total revenue is price × quantity:
\(R = px = x(150 + 10x - x^2)\)
\(= 150x + 10x^2 - x^3\)
The marginal revenue is the derivative of the total revenue:
\( \displaystyle MR = \frac{dR}{dx} = 150 + 20x - 3x^2 \)
At \(x = 10\):
\(MR = 150 + 200 - 300 = 50\)
So the marginal revenue is Rs.50.
Why the other options are incorrect
Option (2) Rs.100 — Incorrect. The marginal revenue at \(x = 10\) is Rs.50.
Option (3) Rs.150 — Incorrect. This is the price per unit, \(p = 150 + 100 - 100 = 150\), not the marginal revenue.
Option (4) Rs.200 — Incorrect. The marginal revenue at \(x = 10\) is Rs.50.
CBSE Applied Mathematics (Class XII):
Marginal Cost and Marginal Revenue
