Ex 6.5, 6 Find the maximum profit that a company can make, if the profit function is given by 𝑝(𝑥) = 41 – 72𝑥 – 18𝑥2The profit function is given by p(x) = 41 − 72x − 18x2 p’(x) = −72 − 36 x Putting p‘ (x) = 0 −72 − 36x = 0 −36x = 72 𝑥 =(−72)/36= −2 Now, P”(x) = −36 Since P” (x) < 0 𝑥=−2 is the maxima ∴ Maximum profit = p(−2) p(x) = 41 − 72x − 18x2 𝑝(−2)=41−72 (−2)−18 (−2)^2 =41+144−18 (4) =41+144−72 =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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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