The demand function for a certain product is such that \(\mathrm{P}(x)=3x^{2}-x+200\), where \(x\) is the number of units of the product demanded and P(\(x\)) is the price per unit.
Marginal revenue when 10 units are sold is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1080
The total revenue is the price per unit times the number of units:
\(R(x) = x\,P(x) = 3x^3 - x^2 + 200x\)
The marginal revenue is its derivative:
\( \displaystyle MR = \frac{dR}{dx} = 9x^2 - 2x + 200 \)
At x = 10:
\(MR = 900 - 20 + 200 = 1080\)
Why the other options are incorrect
Option (1) 59 — Incorrect. This is the derivative of the price, \(P'(10) = 6 \times 10 - 1 = 59\), not of the revenue.
Option (2) 780 — Incorrect. The marginal revenue at x = 10 is 1080, not 780.
Option (4) 4900 — Incorrect. This is the total revenue \(R(10) = 3000 - 100 + 2000 = 4900\), not the marginal revenue.
CBSE Applied Mathematics (Class XII):
Marginal Cost and Marginal Revenue
