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    Question

    Find the maximum people that a company can recruit, if

    the recruit function is given by p(x) = 41 тИТ 24x тИТ 18x2
    A 50 Correct Answer Incorrect Answer
    B 48 Correct Answer Incorrect Answer
    C 49 Correct Answer Incorrect Answer
    D 47 Correct Answer Incorrect Answer

    Solution

    The recruit function is given as p(x) = 41 тИТ 24x тИТ 18x2 Therefore, pтАЩ(x) = - 24 - 36x PтАЩтАЩ(x) = -36 Now, pтАЩ(x) = 0 => x = -24/36 = -2/3 Also, PтАЩтАЩ(-2/3) = -36 < 0 By second derivative test, x = -2/3 is the point of local maxima of p. Therefore, Maximum profit = p(-2/3) => 41 тАУ 24(-2/3) тАУ 18(-2/3)2 ┬а => 41 + 16 тАУ 8 = 49 Hence, the maximum recruit that the company can make is 49 people.

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