CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
A firm's profit function is P(x) = −x² + 60x − 500 (in ₹), where x is the number of units produced. The maximum profit is:
The maximum profit is ₹400. Setting the derivative −2x + 60 to zero gives x = 30 units, and substituting gives −900 + 1800 − 500 = 400. The negative second derivative confirms this is a maximum.
- A₹300
- B₹400Correct
- C₹500
- D₹1,100
Explanation
P'(x) = −2x + 60 = 0 gives x = 30. P(30) = −900 + 1800 − 500 = 400. P''(x) = −2 < 0 confirms a maximum. ₹1,100 wrongly omits the fixed cost term of −500 while ₹300 arises from an arithmetic slip.
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