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Math Help - Lagrangian function.

  1. #1
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    Lagrangian function.

    f(x,y)=2x^2+y^2 subject to the constraint of x+y=1.

    I understand how to set it up and how to find f with respect to x y and L.

    fx=4x+L
    fy=2y+L
    fL=x+y-1

    So, again...I understand the cal part of it, but fail to remember the basic allgebra part. Please solve for x, y, and L (ie the critical point)
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  2. #2
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    set f_x, f_y and f_L = 0 then solve the system.
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  3. #3
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    I know to set them equal to 0, but I'm not exactly sure how to solve from there. This may actually be the wrong section since this is just algebra...
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  4. #4
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    f_x=4x+L=0 ...(1)
    f_y=2y+L=0 ...(2)
    f_L=x+y-1=0 ...(3)

    Using (1) and (2)

    4x+L=2y+L

    Therefore

    4x=2y

    2x=y

    Putting this into (3)

    x+2x-1=0

    3x-1=0

    x=\frac{1}{3}

    Can you solve it from here?
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  5. #5
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    Oh, I feel dumb now... Thank you!
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