A store sells a particular nonperishable product. The demand for the product each day is 1 item with probability 1/6, 2 items with probability 3/6, and 3 items with probability 2/6. Assume that the daily demands are independent and identically distributed. The store uses an (s, S) = (2, 4) policy to manage its inventory: each evening if the remaining stock is less than or equal to s items, the store orders enough to bring the total stock up to S items next morning. These items reach the store before the beginning of the following day. Assume that any demand is lost when the item is out of stock. Assume that each item sells at $150, the variable cost per item is cu = $50, the fixed cost for each order is cf = $100, and the holding cost is $5 for each item held overnight (for accounting). Let Xn be the inventory level at the end of day n. Then X = {Xn : n = 0,1,2,...,} is a discrete time Markov chain. Find the state space S and the transition matrix of the DTMC.