Suppose a coffee shop order and fulfillment process is configured simply as a single queue with twosteps: wait and service. Customers enter, wait their turn, and then are served, by placing andreceiving their order all at once. Suppose that an average of 10 customers per hour enter the coffeeshop while the shop is open.On average, there are two customers waiting in line to place their orders. It takes an average of 2minutes to go through the service step, that is, it takes 2 minutes to complete the second step ofplacing and receiving the order.In steady state,O The average wait time before placing an order is 12 minutes.O The average time between customer arrivals is 5 minutes.O None of the answers are correct.There is an average of one customer being served at a time.O The average total time to wait and be served is 15 minutes.

EXPLANATION : To see why, we can use Little's Law, which states that the average number of customers…

Answered: Suppose a coffee shop order and…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 10 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. On average, how long does a plow wait before the mechanic begins the repair? Group of answer choices 0.17 days 0.53 hours 53 minutes 1.33 hours
Customers arrive in a barber shop at an average rte of five per hour, the actual arrivals being Poisson distributed. There is one barber on duty at all times and there are four chairs for customers who arrive when the barber is busy. Local fire ordinances limit the total number of customers in the shop at the same time to maximum of five. Customers who arrive when the shop is full are denied entrance and their business is presumed lost. The barber's service time is exponentially distributed, but the mean changes with the number of customers in the shop. As the shop fills, the barber tries to speed service, but actually becomes less efficient, as shown in the following table: Number in Shop Mean Service Time, minute 1 9 2 10 Determine: a) the probability that the barber is idle. Answer in 4 decimal places. b) the average number of people in the shop at the same time. Answer in 3 decimal places. 3 12 4 15 5 20
A horologist (watchmaker) is typically able to service a mechanical watch in about 120 minutes (exponential distribution). Assuming an 8 hour work-day, the watchmaker averages 3 customers arriving at his shop every day following a poisson distribution. The watchmaker just purchased a new machine that will polish the dial and crystal reducing his service time by 20 minutes per watch. How much will the line for a watch waiting to be serviced be reduced by the watchmaker using this new machine, assuming no increase in customer demand? O 2.25 watches waiting for service O The number waiting to be serviced will be reduced by about 1.2 watches O The number waiting to be serviced will be reduced by about 0.4 watches The number waiting to be serviced will be reduced by about 1.45 watches
The program coordinator is out of town at a conference and you, as the assistant program coordinator, find yourself besieged by dozens of students needing permission to get into a very popular (but closed) class. Student arrivals are governed by the Poisson distribution with a mean of 5 minutes. Telling the students that they can't get into the closed class takes about 3 minutes, and this average is exponentially distributed. About how long does it take a student to wait in line and receive your valuable service?
You are the manager of a local bank where three tellers provide services to customers. On average, each teller takes four minutes to serve a customer. Customers arrive, on average, at a rate of 40 per hour. Having recently received complaints from some customers that they waited a long time before being served, your boss asks you to evaluate the service system. Specifically, you must provide answers to the following questions: a. The average utilization of the three-teller service system is p= 0.8889. (Enter your response rounded to four decimal places.) b. The probability that no customers are being served by a teller or are waiting in line is Po= 0.0280. (Enter your response rounded to four decimal places.) c. The average number of customers waiting in line is L₁ = customers. (Enter your response rounded to one decimal place.)
On average, a patient spends 5 minutes waiting and 15 minutes being treated at PSH Clinic. Given the average number of patients waiting and being treated at the clinic is 50, what is the average number of patients coming through the clinic per minute on a typical day?
Joe’s market is a small grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane at an average rate of 15 customers per hour and that the average order takes 3 minutes to ring up and bag. If Joe does not want the average waiting time in the queue to exceed 5 minutes, what would you tell Joe about his current system? Back up your statement with quantitative information and assumptions.
Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take, on average, 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. What percentage of time is Judy idle? Note: Round your answer to 1 decimal place. How much time, on average, does a student spend waiting in line? Note: Do not round intermediate calculations. Round your answer to the nearest whole number. How long is the (waiting) line on average? Note: Round your answer to 2 decimal places. What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? Note: Do not round the intermediate calculations. Round your answer to 2 decimal places.
A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. How long does the average person spend waiting for a clerk? 1.143 minutes 3.429 minutes 1.929 minutes 0.643 minute

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