CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
A Chennai manufacturer faces the demand function p = 120 − 0.5x, where p is price in ₹ per unit and x is units sold. At what output is total revenue maximum?
Revenue is price times quantity, giving R = 120x − 0.5x². Its derivative is 120 − x, which is zero at x = 120. The second derivative is negative, so revenue is maximum at 120 units, not at 240, which would be the answer if the 0.5 were ignored.
- A120 units
- B240 unitsCorrect
- C60 units
- D180 units
Explanation
Revenue R = px = 120x − 0.5x². R' = 120 − x. Wait: R' = 120 − x, setting to zero gives x = 120. Checking: R'' = −1 < 0, so it is a maximum at 120 units.
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