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

A firm's total revenue is R = 100x − 2x² and its total cost is C = 20x + 500, both in ₹, where x is the number of units. What is the maximum profit?

The maximum profit is ₹300. Profit is 80x − 2x² − 500, which is maximised at x = 20 where the first derivative is zero and the second is negative. Substituting gives 1,600 − 800 − 500 = ₹300 after deducting the fixed cost.

  1. A₹300Correct
  2. B₹800
  3. C₹1,300
  4. D₹700

Explanation

Profit = 80x − 2x² − 500. Setting dP/dx = 80 − 4x = 0 gives x = 20, and the second derivative −4 is negative, so this is a maximum. Profit = 1,600 − 800 − 500 = ₹300. ₹800 ignores the fixed cost of ₹500.

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