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Ex 6.3, 6 Find the maximum profit that a company can make, if the profit function is given by š‘(š‘„) = 41 ā€“ 72š‘„ ā€“ 18š‘„2The profit function is given by p(x) = 41 āˆ’ 72x āˆ’ 18x2 pā€™(x) = āˆ’72 āˆ’ 36 x Putting pā€˜ (x) = 0 āˆ’72 āˆ’ 36x = 0 āˆ’36x = 72 š‘„ =(āˆ’72)/36= āˆ’2 Now, Pā€(x) = āˆ’36 Since Pā€ (x) < 0 š‘„=āˆ’2 is the maxima āˆ“ Maximum profit = p(āˆ’2) p(x) = 41 āˆ’ 72x āˆ’ 18x2 š‘(āˆ’2)=41āˆ’72 (āˆ’2)āˆ’18 (āˆ’2)^2 =41+144āˆ’18 (4) =41+144āˆ’72 =113 Hence, the maximum profit is 113 unit.

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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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.