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CA Foundation · Quantitative Aptitude · Differential and Integral Calculus

The profit function of a company is P(x) = −x² + 40x − 100 (in ₹), where x is the output in units. The maximum profit is:

Setting dP/dx = 40 − 2x to zero gives x = 20, and the second derivative is −2, which is negative, confirming a maximum. Substituting x = 20 into the profit function gives −400 + 800 − 100 = 300, so maximum profit is ₹300.

  1. A₹20
  2. B₹400
  3. C₹700
  4. D₹300Correct

Explanation

dP/dx = −2x + 40 = 0 gives x = 20, and the second derivative −2 is negative, so this is a maximum. P(20) = −400 + 800 − 100 = 300. The value 20 is the output, not the profit, and 400 ignores the fixed term of −100.

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