Hello!

I have a consumption life cycle problem i need help with.

I need to maximize: G(x1,x2)=log(x1)+log(x2) , where x is the consumption in each period.

I also know that the utility function is the natural logarithm function (i.e. exp(log(x)) =x).

The next step is to set up a Lagrange function for this function, but im not sure if im suposed to use the life cycle problem or the utility function?

should i use the cosumption problem in Lagrange?

Lagrange(x1,x2,,)=log(x1)+log(x2)+(function)+(function

or use the utility function?

Lagrange(x1,x2,,)=x1+x2+(function+(function)