In a corporate office, 3 secretaries use the printer on average every 6 minutes, according to an exponential distribution. On average, the printer performs 15 jobs per hour, according to an exponential distribution. The salary of secretaries is $30 per hour. The current printer maintenance cost is $15 per hour. The manager has noticed that his secretaries waste a lot of time waiting for printouts and is studying the next option.

Add a new, faster printer that prints on average 20 jobs per hour based on an exponential distribution. This way you would have two machines. The old printer will then be used only if the new printer is busy, that is, the old printer will be used exclusively if the new printer is running a job. The maintenance cost for the new printer is $30 per hour.

The manager believes that the secretary is only wasting time while she waits for her work to start printing; printing time is not considered downtime.

a) Construct the rate diagram for the current and proposed system b) Find the steady state probability distribution for the current and proposed situation

c) Which of the two options is the most profitable for the company?