Executives of a large discount drug store are concerned with customers balking from the single check-out lines in their stores because they are waiting too long. The executives have set the objective of increasing sales by improving customer check-out service. For that purpose, they have hired a data analytics consultant.

The consultant has studied the operations of a particular store and has learned the following information. Customers get on the single check-out line in the stores at the mean rate of 28 per hour. Once on the line, customers are then served on a first-come, first-served, basis. On average, one cashier, working alone, can check-out a customer in two minutes. Working together as a team, an additional cashier reduces the check-out time of a customer by 15 seconds, on average. The manager has also discovered that, on average, customers will balk if their wait on the line is five minutes or more. (Assume Poisson arrivals and exponential service times.)

NOTES:

• In this problem, report all probabilities rounded to four decimal places and report all times as minutes and decimal seconds.
• In part 12 you MUST provide a copy of your Excel spreadsheet containing your calculations for problem A to receive credit for this problem. You are also reminded to submit all of your computer files for this problem with your completed

1. In new lines entered below this part, describe the state and/or situation of the waiting line if only a single cashier is working the check-out counter.

2. a.In new lines entered below this part, state the appropriate operating characteristic used as the criterion for this problem.

b.In new lines entered below this part,state algebraically the specific criterion the consultant is using in terms of the operating characteristic stated in part a.

3. In new lines entered below this part, state the minimum total number of cashiers needed to meet the consultant's objective.

With the minimum number of cashiers stated in part 3 all working together as a single team:

4. In new lines entered below this part, state the probability that the check-out line is empty of customers.

5. In new lines entered below this part, state how long, reported in minutes and seconds, is the mean time that customers are expected to have to wait on the check-out line.

6. In new lines entered below this part, on average, state how many customers are expected to be waiting on the line.

7. In new lines entered below this part, state how long, reported in minutes and seconds, is the mean time for a cashier to check-out a customer.

8. In new lines entered below this part, state the chance that a customer will have to wait on the line before being served by a cashier.

9. In new lines entered below this part, state the chance that a customer will be taken by the cashier right away without having to wait at all.

10.In new lines entered below this part, state much time, reported in minutes and seconds, it will take on average for customers to check-out, from the time they arrive on the waiting line until the time they leave the cashier.

11.In new lines entered below this part, state the chance that the check-out line is empty for five minutes so that all the cashiers can take a short break for personal business without being interrupted by the arrival of a customer. (Simply put, state the chance that no customers will arrive in a five-minute period.)

12.In a space created below this part, you must present HERE a copy of your Excel spreadsheet for problem A.