ABC Printing Store provides self-service machines so that students can make last-minute copies of class presentations (either that, or printing 90 copies in the computer lab!). Arrival patterns follow a Poisson distribution. The mean rate is 15 arrivals per hour for this operation. With the current equipment, the average service time is 3 minutes. However ABC is thinking of buying new machines that are available that will reduce this to an average of 2 minutes.
a) ABC currently leases one old copy machine for student self-service. What is the average number of students in system in the current system. If a new machine can be leased to replace the old machine, what will be the new average number of students in system?
b) Instead of leasing the new machine, ABC could lease a second, old machine. What will be the average number of students in system in this case?
c) The average value of time for the students requiring copying is $15 per hour. From the point of view of overall cost of leasing, the option of leasing two old machines is $3 per hour more expensive than the option of leasing one new machine. However, the ABC is mindful of customer’s waiting cost. It wants to choose the option with less total cost i.e (customer cost + service cost). Which is the better option, to lease a new machine or to lease one more old machine?