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

A Jaipur company has total revenue R(x) = 50x - x^2 and total cost C(x) = 10x + 100 (in rupees). At what output is profit maximum?

Profit is maximum at 20 units. Profit equals 40x minus x squared minus 100, its derivative 40 minus 2x is zero at x = 20, and the second derivative is negative, confirming a maximum.

  1. A20Correct
  2. B25
  3. C40
  4. D15

Explanation

Profit = R - C = 40x - x^2 - 100. Its derivative is 40 - 2x = 0, giving x = 20. The second derivative is -2, which is negative, so this is a maximum. 25 comes from ignoring the variable cost of 10 per unit.

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