The total cost (in Rs.) of producing x units of an item is \(C(x) = 2x^{3} - 15x^{2} + 60x + 100\). The marginal cost when 4 units are produced is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 36
The marginal cost is the rate of change of the total cost with respect to the number of units:
\( \displaystyle MC = \frac{dC}{dx} = 6x^{2} - 30x + 60 \)
At x = 4:
\( MC = 6 \times 16 - 30 \times 4 + 60 \)
\( = 96 - 120 + 60 \)
\( = 36 \)
So the marginal cost is Rs. 36.
Why the other options are incorrect
Option (1) Rs. 228 — Incorrect. This is the total cost C(4) = 128 − 240 + 240 + 100 = 228, not its rate of change.
Option (3) Rs. 48 — Incorrect. The marginal cost at x = 4 is C′(4) = 36, not 48.
Option (4) Rs. 60 — Incorrect. This is C′(0), the marginal cost when no units are produced.