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

The marginal revenue function is MR = 50 - 6x and the marginal cost function is MC = 10 + 2x (in rupees). Profit is zero at x = 0. At what output is profit maximised, and what is the maximum profit?

Profit is maximised at 5 units with maximum profit of Rs 100. Equating MR and MC gives x = 5, and integrating marginal profit 40 - 8x gives profit 40x - 4x², which equals 200 - 100 = 100 at x = 5.

  1. Ax = 5, profit Rs 100Correct
  2. Bx = 5, profit Rs 120
  3. Cx = 4, profit Rs 80
  4. Dx = 4, profit Rs 96

Explanation

Set MR = MC: 50 - 6x = 10 + 2x gives x = 5. Marginal profit = 40 - 8x, so profit = 40x - 4x². At x = 5: 200 - 100 = 100. Rs 120 would come from wrongly using 40x - 4x² at a different value.

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