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CA Foundation · Quantitative Aptitude · Differential and Integral Calculus

The cost function of a firm is C(x) = 5x² + 40x + 720. At what output is the average cost minimum?

Average cost is minimised where its derivative is zero. Here AC = 5x + 40 + 720/x, so 5 = 720/x², giving x = 12 units. At this output marginal cost equals average cost, both being ₹160.

  1. A10 units
  2. B12 unitsCorrect
  3. C14 units
  4. D16 units

Explanation

AC = 5x + 40 + 720/x. AC' = 5 − 720/x² = 0 gives x² = 144, so x = 12. AC'' = 1440/x³ > 0, confirming a minimum. Check: at x = 12, MC = 10(12)+40 = 160 and AC = 60+40+60 = 160, equal as expected.

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