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Math Help - compute income

  1. #1
    Micka1
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    compute income

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    Last edited by Micka1; October 2nd 2007 at 10:29 PM.
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  2. #2
    MHF Contributor
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    Price * Number Sold = Total Income.

    x(y) = Price based on number sold = 400 - 0.3y

    y = Number sold

    y*x(y) = Total Income = z(y) = y*(400-0.3y) = 400y - 0.3y^2
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  3. #3
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    z(y)=400y-0.3y^2
    v(y)=4000+6y-.001y^2

    Profit(y) = z(y)-v(y) = 4000 + 394y - 0.299y^{2}

    What do you know about parabolas with negative leading coefficients?

    Since you are to use Differential Calculus,

    \frac{dProfit}{dy} = -0.598y + 394

    Where is that zero?

    -0.598y + 394 = 0 and Solve for y.

    You are beginning to worry me. It seems as though you are a little too eager to give up on a problem if it does not immediately make sense. Maybe it would help to know why you are in this class. Have you had success in the prerequisite mathematics courses?
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Micka1 View Post
    4000 + 394y - 0.299y^2
    Using the quadratic formula gives you
    y=1327.80, y=-10.07
    To find which is the max,
    -0.598y + 394
    substitute y,
    y = 1327.80 = -400.02 y = -10.07= 400.02
    y = 1327.80 = -400.02 is a negative
    therefore 1327.80 is the maximum.
    Any thoughts? Have i got this right?
    What??

    You solve
    \frac{d}{dy}(4000 + 394y - 0.299y^2) = -0.598y + 394 = 0
    to find the critical values of y, just as TKHunny showed you. Then you look at each of these y values in the original equation to see which is the minimum or maximum. (Or you can use the second derivative test.)

    -Dan
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