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Lagrange Multiplier Question

  1. Mar 20, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the product of the maximal and the minimal values of the function
    z = x - 2y + 2xy
    in the region
    (x -1)2+(y + 1/2)2≤2

    2. Relevant equations

    3. The attempt at a solution
    I have taken the partial derivatives and set-up the problem, but I am having difficulty solving for x and y.
    F(x,y) = x-2y+2xy-λ((x -1)2+(y + 1/2)2 -2)
    Fx = 1 - 2y - 2λ(x-1)
    Fy = -2 + 2x - 2λ(y+1/2)
    Fλ = -((x -1)2+(y + 1/2)2 -2))
  2. jcsd
  3. Mar 21, 2012 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    The first two equations are linear in x and y, so you can solve for x and y as functions of λ.

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