Question: Problem 1: Consider a Markov chain {Xnin = 0,1,2 ...} having three states {0, 1, 2} with the following transition probability matrix. At each state,

Problem 1: Consider a Markov chain {Xnin = 0,1,2 ...} having three states {0, 1, 2} with the following transition probability matrix. At each state, you can make one of two actions {1, 2}. For each action taken, transition probabilities are given as follows: Action 1: 11/20 1/27 P(1) = 1/4 1/2 1/4 (1/20 1/2] Action 2: 0 1/2 1/27 P(2) = 1/2 1/4 1/4 (1/2 1/2 0 Each state will be rewarded by the following values. Action 1 2 0 100 150 State 1 200 50 2 -80 10 Formulate the linear programming problem that maximizes the expected average reward

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