Question

A food store has an average of 220 customers arriving per hour during peak shopping hours. During these peak periods all eight checkout counters will be open and operating with a capacity of serving an average of 35 customers per hour per counter. All checkout counters are identical.

A. What proportion of the time would all of the checkout counters and waiting lines be empty of customers?
B. How long would customers wait in line on the average?
C. How many customers would be waiting in each line on the average?

Answer 1

A. What proportion of the time would all of the checkout counters and waiting lines be empty of customers?

1) Total Customer 220 2) Total counters 8 3) Per Counter Average Customer = Total Customer / Total Counters = 220/8 = 27.5 Approx. 28 person 4) Serving capacity of per counter per hours = 35 customers 5) 1 hours means 60 minutes 6) Time required to serve per counter 28 person = 60*28/35 = 48 minutes Therefore, after 48 minutes or 0.80 hrs all counters will be empty of customer.

B. How long would customers wait in line on the average?

1)Serving capacity of per counter per hours = 28 customers 2)Time required to serve per counter 28 person = 48 minutes 3)Average time to serve per customer in counter = 48 minutes /28 Customer = 1.714286 approx. 1.72 minutes Therefore, average waiting time of each customer would be 1.72 minutes

C. How many customers would be waiting in each line on the average?

1) Total Customer 220 2) Total counters 8 3) Per Counter Average Customer = Total Customer / Total Counters = 220/8 = 27.5 Approx. 28 person Therefore, 28 person would be waiting in each counter.