Question

A campus deli serves 300 customers over its busy lunch period from 11:30 a.m. to 1:30 p.m. A quick count of the number of customers waiting in line and being served by the sandwich makers shows that an average of 10 customers are in process at any point in time.Round your answer to 3 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers.

Answer 1

Complete question is;

A campus deli serves 300 customers over its busy lunch period from 11:30 am to 1:30 pm. A quick count of the number of customers waiting in line and being served by the sandwich makers shows that an average of 10 customers are in process at any point in time. What is the average amount of time that a customer spends in process?

Answer:

4 minutes

Step-by-step explanation:

For this question, we will apply Little's law which is is a theorem that determines the average number of items in a stationary queuing system, based on the average waiting time of an item within a system and the average number of items arriving at the system per unit of time.

The formula for the law is:

Inventory = flow rate × flow time.

We are given;

Inventory = 300 customers

flow time is from 11: 30am to 1:30pm which is 2 hours = 120 minutes

Flow rate = 300/120 = 2.5 persons/minute

Now, Making flow rate the subject of the formula earlier given, we have;

flow rate =  inventory/ flow time

Flow time is the time each person spends in the process

Thus, plugging in the relevant values, we get ;

We are told that an average of 10 customers are in process at any point in time.

Thus;

Average flow time = average inventory/flow rate = 10/2.5 = 4 minutes