If the marginal cost function is MC(q) = 3q^2 - 8q + 10 and fixed costs are 50 OMR, find the total cost function C(q).
Answer and explanation
Correct answer: D. q^3 - 4q^2 + 10q + 50
- Step 1: Total cost is the integral of marginal cost: C(q) = integral of MC(q) dq.
- Step 2: Integrate term by term: integral of (3q^2 - 8q + 10) dq = q^3 - 4q^2 + 10q + K.
- Step 3: Fixed costs represent C(0) = 50, so K = 50.
- Step 4: Thus, C(q) = q^3 - 4q^2 + 10q + 50.
Answer
q^3 - 4q^2 + 10q + 50.
Why not the others: '3q^3 - 8q^2 + 10q + 50' neglects dividing by powers during integration; 'q^3 - 4q^2 + 10q' omits the fixed cost constant; '6q - 8 + 50' differentiates rather than integrates MC(q).
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