Skip to content

CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business

A firm's total cost is C = x² + 20x + 400 (in rupees) where x is the number of units. At what output is the average cost per unit minimum?

Average cost is x + 20 + 400/x. Differentiating and equating to zero gives x squared equal to 400, so output is 20 units. The second derivative is positive, so this is a minimum, and at this point average cost equals marginal cost at Rs 60.

  1. A10 units
  2. B20 unitsCorrect
  3. C40 units
  4. D400 units

Explanation

AC = x + 20 + 400/x. Setting dAC/dx = 1 − 400/x² = 0 gives x² = 400, so x = 20. The second derivative 800/x³ is positive, confirming a minimum. At x = 20, AC = 60, which equals MC = 2x + 20 = 60. Choosing 10 would come from solving 1 − 100/x² incorrectly.

Did you get it right without looking?

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

Practise Calculus - Application in BusinessFree diagnostic mock

More Calculus - Application in Business questions