Tim has preferences over consumption in period 1 and 2 of the form u(x1, 12) = 2x;" 4x294. The price of consumption is $1 in both periods. He has $6,000 in the bank now and is trying to decide between two different investment opportunities. A and B. MU=1/2x1-3/4 x23/4 and MU;=3/2x11/4 -1/4 A: invest $5,000 in period 1 and receive $12,000 in period 2. B: invest $1,000 in period 1 and receive $3,000 in period 2. a. If Tim can borrow and lend at a rate of interest of 50 percent, which investment opportunity will he choose? (Assume that Tim cannot invest more than $5000 if he chooses A, or $1000 if he chooses B.) Show your analysis. b. Given your answer in (a), how much will he consume in each period