# solution

Five administrative assistants use an office copier. The average time between arrivals for each assistant is 39 minutes, which is equivalent to an arrival rate of arrivals per minute. The mean time each assistant spends at the copier is 6 minutes, which is equivalent to a service rate of – per minute. Use the M/M/1 model with a finite calling population to determine the following.

(a) The probability that the copier is idle. (Round your answer to four decimal places.)
(b) The average number of administrative assistants in the waiting line. (Round your answer to four decimal places.)
(c) The average number of administrative assistants at the copier. (Round your answer to four decimal places.)
(d) The average time (in minutes) an assistant spends waiting for the copier. (Round your answer to two decimal places.) min

(e) The average time in minutes) an assistant spends at the copier. (Round your answer to two decimal places.) min waiting time? (Round your answers to two decimal places.)

(f) During an 8-hour day, how many minutes does an assistant spend at the copier? How much of this time

total time
waiting time min min

A total of % of the administrative team’s time is spent waiting for the office copier. the sole objective of management were to reduce non-productive waiting time, then management should consider purchasing a second copier.