CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
The total cost of producing x units at Sharma Textiles is C(x) = x^3 - 12x^2 + 60x + 500 rupees. At what output level is the marginal cost minimum?
Marginal cost is minimum at x = 4 units. Marginal cost is 3x^2 - 24x + 60; setting its derivative 6x - 24 to zero gives x = 4, and the positive second derivative of 6 confirms a minimum.
- A2
- B4Correct
- C6
- D12
Explanation
MC = C'(x) = 3x^2 - 24x + 60. Differentiating MC: 6x - 24 = 0 gives x = 4. The second derivative of MC is 6 > 0, so MC is minimum at x = 4. Using x = 6 comes from wrongly minimising C itself or taking 12/2.
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