A campus deli serves 300 customers over its busy lunch period from 11:30 a.m. to
ID: 3167649 • Letter: A
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. What is the average amount of time that a customer spends in process?
One of the chair lifts at a ski resort unloads 1800 skiers per hour at the top of the slope. The ride from the bottom to the top takes 12 minutes. How many skiers are riding on the lift at any given time?
Patients take a drug for severe acne for 6 months and there are 150,000 new patients each month. How many patients are taking this drug on average at any given time?
A large-scale bakery is laying out a new production process for its packaged bread, which it sells to several grocery chains. It takes 12 minutes to bake the bread. How large of an oven is required so that the company is able to produce 4200 units of bread per hour (measured in the number of units that can be baked simultaneously)?
Consider the baggage check-in process of a small airline. Check-in data indicate that from 9 a.m. to 10 a.m., 240 passengers checked in. Moreover, based on counting the number of passengers waiting in line, airport management found that the average number of passengers waiting for check-in was 30. How long did the average passenger have to wait in line?
Explanation / Answer
SOLUTION:
A).
Number of customers served = 300 customers
Corresponding period ( 11.30 AM to 1.30 PM ) = 2 hours = 120 minutes
Thus Rate of customer service = 300 / 120 = 2.5 customers/ minute
Average number of customers in the process = 10
This problem will be solved using Little’s law, which states:
Rate of arrival/service of a process x Throughput time of the process = Total in process inventory in the process
Thus,
Throughput time of the process = Rate of service of the process/ Total in process inventory
Let the average amount of time customer spends in the process ( i.e. Throughput time of the process ) = T
Therefore ,
T = Rate of customer service ( i.e. rate of service of the process)/ Average number of customers in the process ( i.e. Total In process inventory)
Or, T = 120/10 = 12 minute
B).
Number of trips in an hour = 60/12 = 5
Chair lift unloading is 1800 skiers per hour
Number of skiers on the lift at any time= 1800/5 = 360
C).
One month = 150,000 patients
Duration of treating the acne = 6 months = 6 * 30 = 180 days
Patients per day = 15000/30 = 5000 patients per day
Total duration of treatment for 5000 patients = 5000 * 180 = 900,000 days
On average at any given time the number of patients = 900,000/5000 = 180 patients
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