2. (10 points) Suppose that the consumer's preferences are given by 002,1) = x/E+\\/i=c1/2+W2 where c is the level of consumption and l is leisure. The consumer has to allocate 5000 hours between leisure and labour (i.e. h = 5000). The real wage rate (to) is 20 per hour and the real nonwage income (arr) is 800. (a) Compute the Optimal level of consumption and leisure. (b) Conrm that the allocation found in part (a) is in fact optimal by computing the consumption level and the utility if leisure was l'\" 2, I,\" 1, 1*, l'\" + 1, 1* + 2