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

A Chennai manufacturer has revenue R(x) = 50x − x² and cost C(x) = 10x + 100 (in rupees thousands). At what output x is profit maximised?

Profit is maximised at x = 20. Profit equals 40x − x² − 100, its derivative 40 − 2x is zero at x = 20, and the second derivative of −2 confirms a maximum. Setting only marginal revenue to zero would wrongly give 25.

  1. Ax = 25
  2. Bx = 40
  3. Cx = 20Correct
  4. Dx = 30

Explanation

Profit = R − C = 40x − x² − 100. Setting the derivative 40 − 2x = 0 gives x = 20. The second derivative is −2, negative, so it is a maximum. x = 25 comes from setting MR = 0 and ignoring marginal cost.

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