hey I understand the cobb-douglas function but im unsure how you apply the concept to the question given below:

"Solve the optimal consumption problem analytically using the following Cobb-Doublas utility function:$\displaystyle

U=C^{\alpha}_1

C^{1-{\alpha}}_2$ Subscripts 1 and 2 denote present (young) and future (old) periods and $\displaystyle \alpha$ and $\displaystyle 1- {\alpha}$ denote the weighted time preferences for these two periods respectively. "

cheers