In a certain production process, items pass through five manufacturing stages. At the end of each stage, the items are either scrapped with a probability of 0.1, sent through the stage again for rework with a probability of 0.4, or passed on to the next step with a probability of 0.5. Draw the state diagram then solve the following: (a) Describe this as a Markov chain and set up the transition matrix. (b) What is the expected number of steps for a new item entering the first stage either scrapped or completed manufacture? (c) If 972 parts are started in a lot, what is the expected number of good parts that will be completed?