Question: A company currently has one copying machine serving the duplication needs of employees and other. Some complaints about waiting a long time for service have

A company currently has one copying machine serving the duplication needs of employees and other. Some complaints about waiting a long time for service have been reported to the office. A survey was taken and the results indicate that the average arrival rate for copying demand is 10 per hour, and on average, each employee takes 5 minutes to complete his copying work. The arrival process is basically a Poisson process, and the service times follow an Exponential Distribution.

What is the average utilization rate of the copying machine?
What is the average number of people waiting in queue for service?
What is the average waiting time in queue for service?
If the cost of replacing the "old" machine by a new one which has a 25% faster service speed is $160 a day. The cost of waiting is assumed $5.5/per hour/per user with 10 open-hour a day of the library. Would you suggest the director to use the new machine? Why?

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