XYZ is a company who sells mini milling machines to universities for educational purposes. The company observes the number of machines on its hand (call it i) at the beginning of a month. If at the beginning of a month i ≤ 1, then the company orders 3 - i machines (so, the number of inventories is completed to 3). If i ≥ 2, then 0 machines are ordered. It is known that delivery of all ordered machines is immediate. The customers are equally likely to demand 0, 1, 2, or 3 machines from XYZ during the month. After fulfilling these demands, the company observes the inventory level at the beginning of the next month. a. Define the states b. Construct the one-step transition matrix.