CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
The average cost of a Jaipur firm is AC = 2x + 288/x (rupees per unit). At what output is average cost minimum?
Average cost is minimum at 12 units. Differentiating 2x + 288/x gives 2 - 288/x^2; setting it to zero gives x squared as 144, so x is 12, and the positive second derivative confirms a minimum.
- Ax = 6
- Bx = 12Correct
- Cx = 144
- Dx = 24
Explanation
d(AC)/dx = 2 - 288/x^2 = 0 gives x^2 = 144, so x = 12. Second derivative 576/x^3 is positive, so minimum. x = 144 is x^2 mistaken for x.
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