Minimize the function f(U)

Discussion in 'Homework Help' started by jobu180, Sep 10, 2009.

  1. jobu180

    Thread Starter New Member

    Nov 1, 2008
    7
    0
    I'm having problems solving the following problem:
    U1,U2,U3, lamda, B are variables

    f(U)=1.2(U1)^2+[(U2)-(U1)]^2(U2)^2+1.3(U3)^2 subject to the constraints
    (U1)^2+(U3)^2=10
    (U2)+(U3)=1.2

    Using Lagrange multipliers;

    L= 1.2(U1)^2+[(U2)-(U1)]^2(U2)^2+1.3(U3)^2 -lamda((U1)^2+(U3)^2-10) + B((U2)+(U3)-1.2)

    Taking the partial derivative of L (d = partial)

    dL/d(U1) = 2.4(U1)+2(U1)(U2)^2-2(U2)^3= 2(U1)lamda
    dL/d(U2) = 2*(U1)^2*(U2)-6*(U1)(U2)+4*(U2)^2=B
    dL/d(U3) = 2.6(U3)=2(U3)lamda + B
    dL/d(lamda) = (U1)^2+(U3)^2=10
    dL/dB = (U2) + (U3) = 1.2

    Am I on the right track? I'm having trouble solving the problem from here.

    Any help would be appreciated. Thanks,
     
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