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The profit p(x) of a perfume company , in thousands of dollars,is given by p(x)=-5x^2+400x-2550, where x is the amount spent on advertising , in thousands of dollars

a) determine the max profit the company can make
b)Determine the amount spent on advertising that will result in the max profit
c)What amount must be spent on advertising to obtain a profit of at least $4 000 000

  • Math -

    The vertex of a parabola y=ax2 + bx + c occurs at x = -b/2a

    So, when x = 40, we have p(x) = 5450
    Duh. We just said that x = 40. How many dollars does that represent?

    Now we want -5x2+400x-2550 >= 4000

    Think of the parabola. It opens downward. So, the portion above the line y=4000 is just a small cap, where

    22.97 <= x <= 57.03

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