The price per unit of a commodity produced by a company is given by \(\mathrm{P} = 92 - 2x^{2}\), where x is the quantity demanded. The marginal revenue of producing 3 units of such a commodity shall be :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 38
The total revenue is price per unit times quantity:
\(R(x) = x(92 - 2x^{2}) = 92x - 2x^{3}\)
The marginal revenue is its derivative:
\( \displaystyle MR = \frac{dR}{dx} = 92 - 6x^{2} \)
At \(x = 3\):
\(MR = 92 - 6 \times 9 = 92 - 54 = 38\)
Tip: Marginal revenue comes from the revenue \(R = Px\), not from the price function P. Differentiating P itself gives \(-4x = -12\), a common slip.