I have to obtain the optimal levels of $ {C_1}_t^{'},{C_2}_t^{'}, and {K_{t+1}}^{'} $
$$ \max \overline{U} = log{C_1}_t^{'} + \beta log{C_2}_t^{'} $$
subject to constraints:
$$ {C_1}_t^{'} + {K_{t+1}}^{'} = w_t $$ $$ {C_2}_t^{'} = (1 + r_{t+1}){K_{t+1}}^{'} $$ $$ {C_1}_t^{'} \geq 0, {C_2}_t^{'} \geq 0, {K_{t+1}}^{'} \geq 0 $$
My question is: How do I set up the Lagrangian equation? Do I have to rearrange the constraints such that I get rid of $ w_t $ and $ r_{t+1}$ ?