Provide all calculation

1. [5 points] Suppose the lifetime utilitj.r of a. consumer is represented by the utility func tien Up; a) = c x e\". (1} Maximize [1) with respect to c and c' subject to the lifetime budget constraint (2' = (1 +r]we [1 + r)c [2} and prove that the consumer's utility maximizing bundle must satisfy 1+r=2. [3}