CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
A Kolkata firm has revenue R(x) = 50x and cost C(x) = 0.1x² + 10x + 400. At what output is profit maximised?
Profit is maximised where marginal revenue equals marginal cost. MR is 50 and MC is 0.2x + 10, so 0.2x = 40 and x = 200 units. The second derivative of profit is negative, confirming a maximum.
- A200 unitsCorrect
- B100 units
- C400 units
- D250 units
Explanation
Profit P = 50x − 0.1x² − 10x − 400 = 40x − 0.1x² − 400. P' = 40 − 0.2x = 0 gives x = 200. P'' = −0.2 < 0. Using 100 would result from setting 0.1x = 40 incorrectly... check: MR = MC gives 50 = 0.2x + 10, x = 200.
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