Question: A company has a central document-copying service. Arrivals can be assumed to follow a Poisson process, with a mean rate of 15 per hour. It can be assumed that service times are exponentially distributed. With the present copying equipment, the average service time is 3 min. A new machine can be leased that has a mean service time of 2 min. The average wage of the people who bring the documents to be copied is $8 an hour.
a. If the machine can be leased for $5 per hour more than the old machine, should the company replace the old machine?
b. Suppose that the new machine is leased. How much space (e.g., number of chairs) must be provided for people to wait to guarantee that at least 90% of the time, this space will be sufficient?