Lagrange multipliers



Hi,
I have just started my adventure with Maxima. 
I am going to prepare a full course 
of computational microeconomics. 
This course will be based on Maxima. 
I have a problem with the method of Lagrange multipliers. 
Are there any tricks to solve the following system of equations:

kill(all)$
assume(X1>0, X2>0,w1>0,w2>0,Y>0,lambda>0)$
L:(w1*X1+w2*X2)+lambda*(Y -(X1^a)*(X2^b));
eq1:diff(L,X1,1)=0;
eq2:diff(L,X2,1)=0;
eq3:diff(L,lambda,1)=0;
solve([eq1,eq2,eq3],[X1,X2,lambda]);

Best,
Tomek Kopczewski