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1. A small company sells high quality laser printers and they use a simple periodic inventory ordering policy. If there are two or fewer printers in inventory at the end of the day on Friday, the company will order enough printers so that there will be five printers in stock at the start of Monday. (It only takes the weekend for printers to be delivered from the wholesaler.) If there are more than two printers at the end of the week, no order is placed. Weekly demand data has been analyzed yielding the probability mass function for weekly demand given by P{D = d} below. Model the system/situation as a Markov chain where Xn is the inventory at the end of week n. (Note: backorders are not accepted.) 0.05, if d = 0 0.1, if d = 1 0.2, if d = 2 P{D = d} = 0.4, if d = 3 0.1, if d = 4 0.1, if d = 5 0.05, if d = 6 (e) If the inventory currently is 3, what is the expected number of consecutive weeks that it will remain at that level? (f) After 5 weeks how many times we can expect 1 printer to be in the inventory if we start at having 0? (g) In the long term, what is the expected number of times each year that an order is placed? (h) If at the end of week 1 there were two items in inventory, what is the expected number of weeks for the inventory to be four