The computer center at Rockbottom University has been experiencing computer downtime. Let us assume that the trials of an associated Markov process are defined as one-hour periods and that the probability of the system being in a running state or a down state is based on the state of the system in the previous period. Historical data show the following transition probabilities: From Running Down
Running 0.90 0.10
Down 0.30 0.70
A. If the system is initially running, what is the probability of the system being down in the next hour of operation?
B. What are the steady-state probabilities of the system being in the running state and in the down state?

Jiffy printing shops does a lot of printing job for college students. the shop use an average of 25 cases of copy paper each day during the 312 days last year. the shop opens 6 days a week for 52 weeks each year and closes on sundays. each case of paper costs $35. it conducts a count of its paper inventory at the end of every quarter of the year. the table below shows the inventory counting records for last year. inventory end of quarter 1 700 cases end of quarter 2 1,050 cases end of quarter 3 920 cases end of quarter 4 800 cases 1. what's jiffy's cost of goods sold last year? 2. what's jiffy's average aggregate inventory value? 3. what's jiffy's inventory turnover last year? 4. what is the printing shop's weeks of supply last year?