The demand function for a certain product is represented by \( p=35+5x-3x^2 \) , where \( x \) is the number of units demanded and \( p \) is the price per unit. The marginal revenue when 2 units are sold is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 19
Revenue is price × quantity, and the marginal revenue is its derivative.
\( R=px=35x+5x^2-3x^3 \)
\( \displaystyle \text{MR}=\frac{dR}{dx}=35+10x-9x^2 \)
At x = 2:
\( \text{MR}=35+20-36 \)
\( =19 \)
Why the other options are incorrect
Option (1) Rs. 26 — Incorrect. The marginal revenue at x = 2 is Rs. 19, not Rs. 26.
Option (3) Rs. 40 — Incorrect. The marginal revenue at x = 2 is Rs. 19, not Rs. 40.
Option (4) Rs. 33 — Incorrect. This is the price p at x = 2 (35 + 10 − 12 = 33), not the marginal revenue.