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Math Help - Maximization Problem

  1. #1
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    Maximization Problem

    I am trying to find what value X needs to be to make the maximum value for Y, but I am not sure how to do that!

    Code:
    X   |   Y
    ---------
    0.6 | 1112
    0.7 | 1113.5
    0.8 | 1107
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  2. #2
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    x = 0.7?

    If this is not the correct answer, you'll have to provide a better problem statement.
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  3. #3
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    Code:
    ( 80(1-x) + 107 )( 5x + 5 ) = y
    That is the equation I drew up. I need to know what X needs to be so that Y is as high of a number as possible.

    If X = 0.66 then Y = 1113.86
    If X = 0.67 then Y = 1113.89
    If X = 0.68 then Y = 1113.84

    So I know the answer is somewhere between 0.66 and 0.67
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by jennifer92 View Post
    Code:
    ( 80(1-x) + 107 )( 5x + 5 ) = y
    That is the equation I drew up. I need to know what X needs to be so that Y is as high of a number as possible.

    If X = 0.66 then Y = 1113.86
    If X = 0.67 then Y = 1113.89
    If X = 0.68 then Y = 1113.84

    So I know the answer is somewhere between 0.66 and 0.67
    Are you required to use a numerical solution here? Your function y(x) is a quadratic and there is a process you can use for this...completing the square. Can you use this method?

    -Dan
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  5. #5
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    I can solve the problem using any method!
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by jennifer92 View Post
    I can solve the problem using any method!
    Okay, so let me ask you the following... Your problem boils down to finding the maximum of y = -400x^2 + 535x + 935. This is a parabola that opens downward, so it has a maximum. The maximum will lie on the axis of symmetry of the parabola and is, in fact, at the vertex. Can you find the vertex of this parabola?

    -Dan
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  7. #7
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    Quote Originally Posted by topsquark View Post
    Okay, so let me ask you the following... Your problem boils down to finding the maximum of y = -400x^2 + 535x + 935. This is a parabola that opens downward, so it has a maximum. The maximum will lie on the axis of symmetry of the parabola and is, in fact, at the vertex. Can you find the vertex of this parabola?

    -Dan
    How did you convert it to y = -400x^2 + 535x + 935 ?

    And I am not sure what a vertex is. The only information I have is the original formula I gave you.
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  8. #8
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by jennifer92 View Post
    How did you convert it to y = -400x^2 + 535x + 935 ?

    And I am not sure what a vertex is. The only information I have is the original formula I gave you.
    I multiplied your expression out and simplified it. A vertex is a maximum point (up, down, left, or right) on a parabola. This is a Pre-Calculus level question, yes?

    -Dan
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  9. #9
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    Thanks for your help, I got it figured out.
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