Suppose that an investor expects to receive fresh money in the amounts of 8 M, M.... Mr at the beginning of each of the next T months. The objective is to make an investment plan that maximizes the accumulated money at the end of month T. There are two investment opportunities, option 1 and 2. In each month, the investor can invest any amount of money on options without exceeding his available money. In other words, he can invest on one or both options, or not invest at all and there is no requirement that he should invest all his money. Once $ X is invested on option i = 1,2 at the beginning of month t, the investor receives S Xa,, at beginning of month + 1 as a bonus. At the beginning of year t+1, received bonus can be invested in addition to the fresh money that the investor receives. There are no further returns from the investments until the end of month T. If $ X is invested on option i = 1,2 at the beginning of month t, the investor receives 8 X 3, at the end of month T as a return. Model the problem using Dynamic Programming using backward recursion. Hint: While constructing recursive function for a stage, consider the returns from the current stage's decisions that will be received at the end of month T in the current stage's reward. Clearly provide the following with an appropriate notation and verbal explanations: 1. (10 points) Stage 2. (10 points) Decision(s) to make 3. (10 points) State 4. (10 points) Stage transformation (Express the next stage's state in terms of the current stage's state and the decisions made) 5. (10 points) Action space (allowable actions) at each stage 6. (10 points) State space for stage 2