I just need help with D, E, AND F

Possibly, In a year from today, The economy may have two states - "good" and "bad." You can assume that the probability of "good" economic state is 1/3, and the probability of "bad" economic state is 2/3. You have two investment opportunities: (i) risky asset will return you $1.32 in a year from now on each $1 you invest "today" if the economy is in "good" state, and $0.90, if the economy is in "bad" state; (ii) (ii) safe asset will return you $1.02 in a year from now on each $1 you invest "today" in each state of the economy. You current wealth is w0 > 0. You are an expected utility maximizer, and your utility of wealth is u(w) = In w. You want to invest your wealth in the optimal way. Suppose you invest the fraction a of your wealth in the risky asset, and the fraction 1 - a in the safe asset. (a) What wealth will you have in a year from now in each state of the economy? (b) What will be your expected wealth? (c) What will be your expected utility of wealth? (d) Which a will maximize your expected utility? (e) How does the optimal fraction of your wealth a invested in the risky asset depend on your current wealth? (f) How does the optimal amount of money awo invested in the risky asset depend on your current wealth