14.5. A company has a central document-copying service. Arrivals are assumed to follow the Poisson probability distribution, with a mean rate of 15 per hour. Service times are assumed to follow the exponential distribution. With the pres- ent copying equipment, the average service time is 3 minutes. A new machine is available that will have a mean service time of 2 minutes. The average wage of the people who bring the documents to be copied is $8 an hour.

a. If the new machine can be rented for $10 per hour more than the old ma- chine, should the company rent the new machine? Consider lost productive time of employees as time spent waiting in queue only because the copying machine is a self-serve device.

b. For the old copying machine, what is the probability when a person arrives that he or she will encounter people already waiting in line for service? (Be careful to identify properly the number of customers who might be present for this situation to arise.)

c. Suppose the new copying machine is rented. How many chairs should be provided for those waiting in line if we are satisfied when there will be enough chairs at least 90 percent of the time?