The demand function for a certain product is represented by the equation \( p=150+12x-x^2 \), where \( x \) is the number of units demanded and \( p \) is the price per unit. The marginal revenue when 5 units are sold is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs. 195
Total revenue = price per unit × number of units:
\( R(x)=px=150x+12x^2-x^3 \)
Marginal revenue is the derivative of total revenue:
\( \displaystyle MR=\frac{dR}{dx}=150+24x-3x^2 \)
At x = 5:
\( MR=150+24(5)-3(25) \)
\( MR=150+120-75=\text{Rs. }195 \)
Tip: Marginal revenue comes from the revenue function R = px, not from the demand (price) function p; differentiating p directly is the usual trap.