A store sells refrigerator and a check the sales database to determine the weekly refrigerator sales. Store manager realize that the demand for the product is zero or one or two refrigerator in a week. He checks last 100 weeks and assumes that demand distribution can be calculated by using following table. Weekly demand 1 Number of weeks 50 2 20 The store uses the following inventory policy: Store manager checks the inventory level at the end of every week. If the inventory level is less than or equal to 1, store manager orders up to 3 units. Otherwise she does not order. Refrigerators are delivered at beginning of next week. This policy is called (R, s, S). In this question R = 1 week, s = 1, and S = 3. Manager also asssumes that unsatisfied demand is lost. a) (10 points) Could you model the above problem as a Markov Chain? Do you think the stationarity assumption is reasonable for your model? Explain. b) (15 points) Define X, that shows the number of refrigerators at the end of the week and Identify the state space. Explain how you define the states. c) (10 points) Draw the transition diagram and write down the P matrix. d) (15 points) If the store end up with 2 products in the last two weeks, what is the probability that store end up with one product back to back 2 weeks and end up with full inventory(3 products) in the last week?