The marginal cost of producing x units of a commodity is MC = 2x + 5 (in Rs.) and the fixed cost is Rs. 24. The average cost of producing 4 units is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 15
The total cost is the integral of the marginal cost, and the constant of integration is the fixed cost:
\( \displaystyle C(x) = \int (2x + 5)\,dx = x^2 + 5x + k \)
At x = 0 the cost is the fixed cost, so k = 24:
\(C(x) = x^2 + 5x + 24\)
\(C(4) = 16 + 20 + 24 = 60\)
The average cost is the total cost per unit:
\( \displaystyle \text{AC} = \frac{C(4)}{4} = \frac{60}{4} = 15 \)
Why the other options are incorrect
Option (1) Rs. 13 — Incorrect. This is the marginal cost at x = 4, \(2(4) + 5\), not the average cost.
Option (2) Rs. 60 — Incorrect. This is the total cost of 4 units; it has not been divided by 4.
Option (4) Rs. 9 — Incorrect. This leaves out the fixed cost: \(\frac{16 + 20}{4} = 9\).