You have two alternative investment opportunities and you have a total of $10,000 to invest. The first will increase the amount invested by 60% with probability 0.6, or decrease it by 40% with probability 0.4. The second will increase the amount invested by 10% for certain. You wish to split the $10,000 between the two opportunities.

1. a)Assuming your utility function is U(x) = 5 + sqrt(x), how much should you put in each investment to maximize your expected utility?
2. b)Assuming your utility function is U(x) = 5 + 2x, how much should you put in each investment?