# Lagrangian in Ramsey model

I struggle to write and solve Lagrangian in the Ramsey model.

I have the following individual preferences with a budget constraint:

and an additional constraint that is a no-ponzi condition:

How to state a Lagrangian in this problem and solve FOC wrt. c_t, a_t+1 and a_T+1???

I tried to combine the two budget constraints:

and then my Langrangian looks like this:

But, I´m not sure that´s correct, because my task says that additional Lagrangian multiplier should be added......