CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
A monopolist faces the demand function x = 60 − 0.5p and has total cost C(x) = 20x + 100, where p is price in ₹ and x is quantity. The profit-maximising price (in ₹) is:
The profit-maximising price is ₹70, which is not correctly keyed in the options.
- A₹50Correct
- B₹60
- C₹70
- D₹40
Explanation
From demand, p = 120 − 2x. Revenue R = 120x − 2x². Profit = 100x − 2x² − 100. P' = 100 − 4x = 0 gives x = 25; P'' = −4 < 0. Price = 120 − 50 = ₹70. So the correct price is ₹70, not ₹50.
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