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 560 small tools per day with an average of 430. 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? (Round the final answer to the first decimal place.)
A) 1.0
B) 3.3
C) 4.3
D) 5.3

Question

Quizplus · Accepted Answer

The average waiting time is the average number of customers in the system divided by the average arrival rate. The average number of customers in the system is the average number of orders in the system plus the average number of orders being served. The average number of orders in the system is the average demand per day divided by the average service rate per day. The average service rate per day is the number of orders served per day divided by the average service time per order. The average service time per order is 1 minute. The average demand per day is 430 orders. The average number of orders served per day is 8 hours per day * 60 minutes per hour / 1 minute per order = 480 orders per day. Therefore, the average number of orders in the system is (430 orders / 480 orders per day) + (480 orders / 480 orders per day) = 1.875 orders. The average waiting time is 1.875 orders / 430 orders per day = 0.00436 hours per order = 4.36 minutes per order.

The Tool Crib at a Large Manufacturing Company Is Responsible