Skip to content

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

For a Chennai firm, the average cost function is AC = x + 400/x + 20 (rupees per unit), where x is the number of units. At what output is average cost minimum, and what is that minimum average cost?

Average cost is minimum at 20 units, where it equals Rs 60. Setting the derivative 1 minus 400 over x squared to zero gives x = 20, and substituting gives 20 + 20 + 20 = 60.

  1. Ax = 20, AC = 60Correct
  2. Bx = 20, AC = 40
  3. Cx = 400, AC = 421
  4. Dx = 10, AC = 70

Explanation

Differentiate: 1 - 400/x^2 = 0 gives x = 20. The second derivative 800/x^3 is positive, so it is a minimum. AC = 20 + 20 + 20 = 60. Option 40 drops the constant 20.

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