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




The profit function is given by P(x) = 72+42š‘„āˆ’š‘„^2 Finding Pā€™(š’™) Pā€™(x) = 42 ā€“ 2x Putting Pā€™ (x) = 0 42 ā€“ 2x = 0 42 = 2x x = 42/2 x = 21 Finding Pā€™ā€™(x) Since Pā€™(x) = 42 ā€“ 2x āˆ“ Pā€(x) = āˆ’2 Since Pā€ (x) < 0 š‘„=21 is the maxima Since pā€™(x) = 42 ā€“ 2x āˆ“ pā€(x) = āˆ’2 Maximum profit = P(21) =šŸ•šŸ+šŸ’šŸš’™āˆ’š’™^2 =šŸ•šŸ+šŸ’šŸ (šŸšŸ)āˆ’(šŸšŸ)^šŸ =72+882 āˆ’441 =72+441 =šŸ“šŸšŸ‘ Hence, Maximum profit is Rs 513

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.