Vermont General Hospital has limited the use of its pharmacy so that it is used exclusively for nurses' prescription orders for medications. Nurses' prescription orders occur at an average rate of 25 orders per hour. The time between consecutive prescription orders, as well as the time to fill a nurse's prescription order follow an exponential distribution. Each pharmacist can process 15 nurse prescription orders per hour. The pharmacy is staffed by two pharmacists who work independently of one another. The prescription-order requests are collected in a common bin located on the counter at the entrance to the pharmacy and are processed in first-come, first-served order. After submitting a request, each nurse waits at the counter until his/her prescription order is filled. (You must show work to all parts of this question to receive credit.)
Answer each of the following questions. Maintain at least three decimal places in your intermediate calculations and round your final answers to 2 decimal places.
1. On the average, how many nurses would be at the counter, including those whose prescription order is in the process of being filled by a pharmacist?
2. On the average, how long does each nurse wait at the counter (including the time for the prescription order to be filled)?
3. What is the probability that there are no nurses waiting at the pharmacy counter?
4. Suppose that the cost to staff one pharmacist in the pharmacy is $90 per hour, and that this cost increases proportionally with the number of pharmacists. Suppose also that the cost to have a nurse waiting at the pharmacy is $45 per hour. Should the pharmacy be staffed with two, three, or four pharmacists to minimize total cost?