Problem 2 Each year Mr. Fontanez has the chance to invest in two different no-load mutual funds the Go-Go Fund or the Go-Slow Mutual Fund. At the end of each year, Ms. Fontanez liquidates her holdings, takes her profits, and then reinvests. The yearly profits of the mutual funds depend on where the market stood at the end of the preceding year. Recently the market has been oscillating around the 12 000 mark from one year end to the next, according to the probabilities given in the following transition matrix: 11,000 12.000 100 0.3 02 120000 05 0.4 1300002 04 0.4 Each year that the market moves up (down) 1,000 points, the Go-Go Fund has profits (losses) of $20,000, while the Go-Slow Fund has profits (losses) of $10,000. If the market moves up (down) 2,000 points in a year, the Go-Go Fund has profits (losses) of $50,000, while the Go-Slow Fund has profits (losses) of only $20,000. If the market does not change, there is no profit or loss for either fund. Ms Fontanez wishes to determine her optimal investment policy in onder to maximize her (long-run) expected average profit per year (1). Identify the state and action (2). Collect all information into the state action table set (3). Determine the optimal policy with respect to the long-run expected profit per year criterion. (Hint: You can solve this by the brute fonce method. But there may exist a way to find it without any computation. If you use this method to identify the optimal policy, please explain why this gives you an optimal policy) (4). Set up the linear programming formulation for this MDP