Tim has preferences over consummion in period 1 and 2 of the form \"(351,172) = 2xll'r4x23\". The price of consumption is $1 in both periods. He has $6,000 in the bank now and is trying to decide between two diffemnt investment opportunities, A and B. MU1=1/2x1'3"4 X23\" and MU2=3/2xi \"4 x2414: 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