Minimize the function f(U)

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jobu180

Joined Nov 1, 2008
7
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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