Suppose that at any period of time a photo-copier machine can either be working properly, in need of maintenance, in need of minor repair, or in need of major repair. If the photocopier is working, the chances that it will require maintenance, minor repair, or major repair in the next time period are respectively 0:15, 0:05, 0:03. Assume that the probability that the maintenance is successfully done in the next period is 1, the probability that the minor repair is successfully done in the next period is 0:8, and the probability that the major repair is successfully done in the next period is 0:5. Construct a Markov Chain and its steady-state probabilities that would allow you to answer the following question: If the owner of the photocopier has to pay $10 for every period that it is not working properly, what is the expected cost per period of the photocopier?