CMA Final · Strategic Cost Management · Business Application of Maxima and Minima
A manufacturer sells x units at a fixed price of Rs 60 per unit. Total cost is C(x) = 0.5x^2 + 10x + 200. To maximise profit, the firm should produce:
Under a fixed price, profit is maximised where price equals marginal cost. Marginal cost is x + 10, so 60 = x + 10 gives x = 50 units. The second derivative is negative, confirming a maximum, and profit is Rs 1,050.
- A25 units
- B50 unitsCorrect
- C60 units
- D10 units
Explanation
Profit = 60x - 0.5x^2 - 10x - 200 = 50x - 0.5x^2 - 200. Derivative 50 - x = 0 gives x = 50. Equivalent to price = MC: 60 = x + 10. Profit at 50 = 2,500 - 1,250 - 200 = 1,050 (positive). The 25-unit option halves the correct answer by mistake.
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