3. Your investment company offers you an opportunity to invest in either of two options (A or B) at the beginning of each of the next 3 years. Both options require an investment of $5,000 and have uncertain returns. For investment option A you will either lose your money entirely or (with higher probability) get back $10,000 (i.e., a profit of $5,000) at the end of the For investment option B you will get back either just your $5,000 or (with low probability) $10,000 at the end of the year. The probabilities for these events are as follows: year. Amount Investment Returned ($) Probability 0 0.3 A 10,000 0.7 5,000 0.9 B 10,000 0.1 You can invest only $5,000 in each year provided you have accumulated that much in hand. Any additional money accumulated is left idle. You are allowed to make only (at most) one investment each year. No partial investment options are allowed. Suppose you have $5,000 to invest at the beginning of the first year. (a) (points: 5+6+1) Use dynamic programming to find the investment policy that maxi- mizes the expected amount of money you will have after 3 years. Specify stages, states, decision variables, the interpretation of the value function, its recursive relationship, the optimal value function, and show the intermediate steps of the solution procedure. Identify the optimal investment policy and the optimal expected amount of money that you will have. 3. Your investment company offers you an opportunity to invest in either of two options (A or B) at the beginning of each of the next 3 years. Both options require an investment of $5,000 and have uncertain returns. For investment option A you will either lose your money entirely or (with higher probability) get back $10,000 (i.e., a profit of $5,000) at the end of the For investment option B you will get back either just your $5,000 or (with low probability) $10,000 at the end of the year. The probabilities for these events are as follows: year. Amount Investment Returned ($) Probability 0 0.3 A 10,000 0.7 5,000 0.9 B 10,000 0.1 You can invest only $5,000 in each year provided you have accumulated that much in hand. Any additional money accumulated is left idle. You are allowed to make only (at most) one investment each year. No partial investment options are allowed. Suppose you have $5,000 to invest at the beginning of the first year. (a) (points: 5+6+1) Use dynamic programming to find the investment policy that maxi- mizes the expected amount of money you will have after 3 years. Specify stages, states, decision variables, the interpretation of the value function, its recursive relationship, the optimal value function, and show the intermediate steps of the solution procedure. Identify the optimal investment policy and the optimal expected amount of money that you will have