The ADJO Police Department participates in a work-release program in which prisoners may work at the county dairy show, which has two entrance gates where patrons pay for tickets before entering the event. Customers visit the entrances and purchase tickets at a rate of 47 per hour. The entrances typically serve an average rate of 51 people per hour. Further, ADJO estimates that waiting costs of being in the queue are $2.00 per hour. Work release for the prisoners does not occur during weekends. Further, work release for the prisoners only occurs during the day shift (assuming a 12-hour shift). For the checkout counter, assuming the Poisson and exponential distributions, answer the following questions using the formulae presented within Table 11.1:
a. What is the average rate of serviced consumers per hour?
b. What is the average rate of consumer arrivals?
c. How many channels are present?
d. What is the average quantity of consumers within the system?
e. What is the average time a consumer spends in the system?
f. What is the average quantity of consumers within the queue?
g. What is the average time a consumer spends in the queue?
h. What is the utilization factor?
i. What is the probability that no consumers are in the system?
j. Perform a simple economic and financial analysis using cost as a basis.
Text Book: Economic and Financial Analysis for Criminal Justice Organizations By Daniel Adrian Doss, William H. Sumrall III, David H. McElreath, Don W. Jones.