Skip to content

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

A Pune firm's total cost function is C(x) = 2x² + 40x + 5,000 (in rupees), where x is units produced per week. At what output is the average cost per unit minimum?

Average cost is minimised at 50 units. Differentiating AC = 2x + 40 + 5000/x and equating to zero gives x² = 2,500, and the positive second derivative confirms a minimum. Equivalently, at this point marginal cost equals average cost.

  1. A40 units
  2. B50 unitsCorrect
  3. C25 units
  4. D100 units

Explanation

Average cost AC = 2x + 40 + 5000/x. Setting dAC/dx = 2 - 5000/x² = 0 gives x² = 2,500, so x = 50. Second derivative 10000/x³ is positive, so it is a minimum. Using x = 100 would come from equating wrongly to 10,000 rather than 2,500.

Did you get it right without looking?

One question tells you little. A timed set on Business Application of Maxima and Minima shows your real accuracy, how long you take and where you lose marks.

Practise Business Application of Maxima and MinimaFree diagnostic mock

More Business Application of Maxima and Minima questions