Question 23 (Choice 2) - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Feb. 10, 2025 by Teachoo

Find the maximum profit that a company can make, if the profit function is given by P(x)=72+42x-x^2, where x is the number of units and P is the profit in rupees.

This question is similar to Ex-6.5, 6 Chapter 6 Class 12

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Transcript

The profit function is given by P(x) = 72+42𝑥−𝑥^2 Finding P’(𝒙) P’(x) = 42 – 2x Putting P’ (x) = 0 42 – 2x = 0 42 = 2x x = 42/2 x = 21 Finding P’’(x) Since P’(x) = 42 – 2x ∴ P”(x) = −2 Since P” (x) < 0 𝑥=21 is the maxima Since p’(x) = 42 – 2x ∴ p”(x) = −2 Maximum profit = P(21) =𝟕𝟐+𝟒𝟐𝒙−𝒙^2 =𝟕𝟐+𝟒𝟐 (𝟐𝟏)−(𝟐𝟏)^𝟐 =72+882 −441 =72+441 =𝟓𝟏𝟑 Hence, Maximum profit is Rs 513

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 15 years. He provides courses for Maths, Science and Computer Science at Teachoo

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