PLEASE DO QUESTION 7-11.

Executives of a large retail store are concerned with customers leaving 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 is five minutes or more. (Assume Poisson arrivals and exponential service times.)

WHAT I HAVE DONE SO FAR (PLEASE CHECK):

7. state how long, in minutes and seconds, is the mean time for a cashier to check-out a customer.

8. state the chance that a customer will have to wait on the line before being served by a cashier.

9. state the chance that a customer will be taken by the cashier right away without having to wait at all.

10. state long, 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. 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.)

I ALREADY HAVE QUESTION 3-6 COMPLETED. NEED HELP WITH 7-11!!!

# 3. State the minimum fotal mumber of cashiers needed to meet the consultant's objective. 1 13 cashies are cred Anwal rate 7 - 23, Service rate p - 40 per box W-28-40"(40-28) -0.05833 hours - 3.5 min. Therefore, 3 casiers are needed to meet the service goal of waiting time of 5 minutes With the minimum number of cashiers stated in part 3 all working together as a single team 4. state the probabilty that the check-out line is empty of customers. c. 1-(28/30) - 0.067 or 6.67% 5. state how long in minutes and seconds, is the mean time that customers are expected to have to wait on the check-out fine. 4. 2830(30-28) - 467 or 28.02 minutes or 1681 seconds 6. on average, state how many customers are expected to be waiting on the line. (28230(30-28) - 13.0667 or 13 customers