The Westland Title Insurance Company leases one copying machine for $45 per day that is used by all individuals at its office. An average of five persons per hour arrive to use this machine, with each person using it for an average of eight minutes. Assume that the inter-arrival times and copying times are exponentially distributed.
a. What is the probability that a person arriving to use the machine will find it idle?
b. On average, how long will a person have to wait before getting to use the machine?
c. On average, how many people will be using or waiting to use the copy machine?
d. Suppose that the people who use the copy machine are paid an average of $9 per hour. On average, how much does the company spend in wages during each eight-hour day paying the people who are using or waiting to use the copy machine?
e. If the company can lease another copying machine for $45 per day, should they do it?