CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The demand function of a product is p = 120 − 2x, where p is the price in ₹ and x the units sold. At what output is total revenue maximum?
Revenue is R = 120x − 2x². Setting marginal revenue 120 − 4x to zero gives x = 30, and the second derivative is negative, so revenue is maximum at 30 units.
- A20 units
- B30 unitsCorrect
- C60 units
- D40 units
Explanation
Revenue R = px = 120x − 2x². R' = 120 − 4x = 0 gives x = 30. R'' = −4 < 0, so it is a maximum. Choosing 60 comes from setting price to zero, which is the wrong condition.
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