CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
A monopolist faces the demand curve p = 120 − 2x and has total cost C = x² + 30x + 100 (₹). What is the maximum profit?
The maximum profit is ₹575. Equating marginal revenue 120 − 4x with marginal cost 2x + 30 gives x = 15 and price ₹90. Revenue is ₹1,350 and total cost is ₹775, so profit is ₹575.
- A₹575Correct
- B₹675
- C₹775
- D₹1,350
Explanation
MR = 120 − 4x and MC = 2x + 30. Setting MR = MC gives 6x = 90, so x = 15, and p = 90. Revenue = 1,350. Cost = 225 + 450 + 100 = 775. Profit = 1,350 − 775 = ₹575. ₹675 omits the fixed cost of ₹100.
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