CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
A company's total cost is C = 2x² − 16x + 128 (₹), where x is the output in units. What is the minimum value of the average cost per unit?
The minimum average cost is ₹16 per unit. Dividing cost by x gives AC = 2x − 16 + 128/x. Setting its derivative to zero gives x = 8, and the positive second derivative confirms a minimum. Substituting gives 16 − 16 + 16 = ₹16.
- A₹16Correct
- B₹8
- C₹32
- D₹128
Explanation
AC = 2x − 16 + 128/x. dAC/dx = 2 − 128/x² = 0 gives x² = 64, so x = 8. The second derivative 256/x³ is positive, so it is a minimum. AC = 16 − 16 + 16 = ₹16. ₹8 is the output level, not the cost.
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