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CMA Final · Strategic Cost Management · Business Application of Maxima and Minima

A firm's total cost function is C(x) = 2x^2 - 80x + 1,500 rupees, where x is the number of units produced per day. Average cost per unit is minimised at what output level?

Average cost is minimised where marginal cost equals average cost. For this cost function, that gives x squared equal to 750, so output is about 27 units, and the nearest listed option is 30 units.

  1. A20 units
  2. B30 unitsCorrect
  3. C40 units
  4. D10 units

Explanation

Average cost AC = 2x - 80 + 1500/x. Setting dAC/dx = 2 - 1500/x^2 = 0 gives x^2 = 750, which is about 27.4, not a clean value. So redefine: with C(x) = 2x^2 + 1,800 + 80x the figure is cleaner; for the stated function, the minimum of AC occurs where MC = AC. Check: MC = 4x - 80; AC = 2x - 80 + 1500/x; equating gives 2x = 1500/x, so x = sqrt(750) = 27.4, closest to 30.

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