At the start of the first week, a construction worker receives a wage offer of ar dollars per week. She may either work at that wage for the entire week or instead seek alternative employment. If she decides to work for that offer in the current week, then at the start of the next week, with probability pi she will have the same offer available, while with probability 1 - pi she will be unemployed (which implies no wages that week as she seeks new employment). If he seeks alternative employment (either because she is dissatisfied with her current wage or because she is currently unemployed), she receives no income in the current week and obtains a wage offer of 1.5r dollars with probability p2 and 0.8r dollars with probability 1 - p2. Note that x is the wage he is offered in the first week. Thus, if she decides to seek emplovment, then regardless of her current wage, she might receive a wage offer of 1.5r with probability p2 or 0.8ar with probability 1 - p2 in the next week . (10 points) Draw the decision tree for the first two weeks, clearly labeling the probabilities as well as the rewards. For a full solution, indicate decisions made in weeks 1 and 2 as well as week 3's terminal conditions . (15 points) Formulate the worker's decision problem as a Markov decision process, in which her objective is to maximize the total expected wages over the next 2 weeks. Assume there is no terminal reward. You will receive full marks for clearly indicating the five basic componenents of this MDP. · (15 points) Let the worker start the 2-week period with an offer of x = $1000. Let P1 be 0.8 and p2 be 0.4. Assume no terminal reward. Should he seek a new job on the first week of employment or take the current offer?