The average cost function for a commodity is given by \(AC = 0.05x^2-5x+1000+\displaystyle\frac{3000}{x}\) in terms of output \(x\). The fixed cost is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3000
Total cost = average cost × output:
\( TC = x \cdot AC \)
\( = 0.05x^3 - 5x^2 + 1000x + 3000 \)
The fixed cost is the part of the total cost that does not depend on x (the value of TC at x = 0):
\( \text{Fixed cost} = 3000 \)
Why the other options are incorrect
Option (1) 1000 — Incorrect. 1000 is the constant term of AC, but in TC it becomes 1000x, which varies with output.
Option (3) 5 — Incorrect. 5 is a coefficient in AC; it gives the variable term \(-5x^2\) in TC.
Option (4) 0.05 — Incorrect. 0.05 is a coefficient in AC; it gives the variable term \(0.05x^3\) in TC.