An office employs several clerks who create documents and one operator who enters the document information in a computer system. The group creates documents at a rate of 25 per hour. The operator can enter the information with an average exponentially distributed time of two minutes. Assume the population is infinite, arrivals are Poisson, and queue length is infinite with FCFS discipline.

a. Calculate the percentage utilization of the operator.

b. Calculate the average number of documents in the system.

c. Calculate the average time in the system.

d. Calculate the probability of four or more documents being in the system.

e. If another clerk were added, the document origination rate would increase to 30 per hour. What would the expected average number of documents in the system become? Show why.