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

A Chennai manufacturer has revenue R(x) = 80x - x^2 and cost C(x) = 10x + 200, both in rupees, for x units. Find the output that maximises profit.

Profit is maximised at 35 units. Profit equals 70x - x^2 - 200; its derivative 70 - 2x is zero at x = 35, and the negative second derivative confirms a maximum. Maximising revenue alone would wrongly give 40 units.

  1. Ax = 70
  2. Bx = 40
  3. Cx = 35Correct
  4. Dx = 30

Explanation

Profit = R - C = 70x - x^2 - 200. Differentiating: 70 - 2x = 0, so x = 35. Second derivative is -2, a maximum. x = 40 results from maximising revenue alone, ignoring the variable cost.

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