Please clearly state all parts. Thanks

Question 2 [15 points] Consider a risk averse individual who has utility function u(a) which is increasing with 11(0) = 0. There is one safe asset which gives $1 for every dollar invested. There are two risky assets: A,B. For A, every dollar invested gives return $0 with probability 2/3 and $3 with probability 1/3. For B, every dollar invested gives return is $0 with probability 2/5 and $3 with probability 3/5. The individual has $45 to invest. Out of $45, the individual must invest $15 in the safe asset and the remaining $30 can be invested in risky assets. Consider two investment choices: (I) invest entire $30 in A and (2) invest $15 in A, $15 in B. (a) [3 points] Drawing diagram of the utility function and showing your work, determine the expected utility of the individual from choice 1. (b) [3 points] Drawing diagram of the utility function and showing your work, determine the expected utility of the individual from choice 2 when return from A is bad. (c) [3 points] Drawing diagram of the utility anction and showing your work, determine the expected utility of the individual from choice 2 when return from A is good. (d) [3 points] Drawing diagram of the utility Jnction and showing your work, determine the expected utility of the individual from choice 2. (e) [3 points] Comparing expected utility cm choices 1,2 in a diagram, determine which choice is better