The service rate can be increased or decreased in increments of $50$ prescriptions per hour. The expense associated with each $50-$prescription increment is $$100.$ In other words, to be able to process $50$ additional prescriptions will cost an additional $$100$ per hour. If the current rate of processing or service is lowered by $50$ prescriptions per hour, the savings are $$100$ per hour. Using queuing theory, describe this service system. What is: e$.$The average time $($hours$)$ a patient spends in the queue waiting?

f$.$ The probability that a patient, upon arrival,must wait?The following data have been collected from a hospital pharmacy. This service

system operates as a single server, single channel system.

The service rate can be increased or decreased in increments of $50$ prescrip$-$

tions per hour. The expense associated with each $50-$prescription increment

is $$100.$ In other words, to be able to process $50$ additional prescriptions will

cost an additional $$100$ per hour. If the current rate of processing or service

is lowered by $50$ prescriptions per hour, the savings are $$100$ per hour. Using

queuing theory, describe this service system. What is:

$($Questions$)$

d$.$ The average number of patients in the queue waiting for service?

e$.$ The average time $($hours$)$ a patient spends in the queue waiting?

f$.$ The probability that a patient, upon arrival, must wait?

Given the associated costs, should the service rate be changed? What are the financial implications associated with your recommendations?