Answer the following questions using the information below:
The tool crib at a large manufacturing company is responsible for providing tools to the factory workers on demand. The tool crib has a variable demand. Historically, its demand has ranged from 300 to 500 small tools per day with an average of 400. Diane, the tool crib attendant, works eight hours a day, five days a week. Each order is for one small tool and each small tool takes Diane 1 minute to retrieve from the bins.
-What is the average waiting time,in minutes?
A) 1.0
B) 1.5
C) 2.5
D) 3.5

Question

Quizplus · Accepted Answer

The average demand is 400 small tools per day. If we divide this by the number of minutes Diane works per day (480, which is 8 hours x 60 minutes), we get the average demand rate of about 0.83 small tools per minute. 
Using the formula for average waiting time in a queuing system (Wq = Lq/λ), where Wq is the average waiting time, Lq is the average number of customers waiting in line, and λ is the arrival rate of customers, we can calculate the average waiting time as follows:

Lq = (0.83/2)^2 / (1 - 0.83/2) ~~ 0.08 
(we use the formula for Lq in an M/M/1 queuing system)

Wq = Lq/λ = 0.08/0.83 = 0.096 = 5.8 minutes.

However, since each tool takes 1 minute to retrieve, we need to subtract that time from the waiting time:

Wq = 5.8 - 1 = 4.8 minutes.

Therefore, the average waiting time is about 4.8 minutes per customer. Rounded to the nearest half minute, this is 2.5 minutes. Therefore, the best choice is C) 2.5.

Answer the Following Questions Using the Information Below