A store open 24 hours per day is interested in determining store traffic. They found that customers arrive uniformly at the rate of 10 customers per hour. The store has asingle worker to process customers. The worker takes an average of 5 minutes to process a customer. If we assume that every customer must be processed, what is theaverage number of customers in the store?For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).10ptAIs...BIUSParagraphOpen Sans,s..E = = E E. Ex2 X2

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Answered: A store open 24 hours per day is…

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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In a coffee shop, there are 4 baristas serving customers standing in a single queue. Customers arrive every 6 minutes on average, and one barista can serve an order in an average of 20 minutes. Customers’ arrivals tend to follow a Poisson distribution and service times tend to be negative exponential. The hourly salary of a barista is $10 per hour, but owner loses about $10 per hour of customer waiting for a barista to take an order. The average time (in hours) that customers must wait before a barista takes their orders. (please round your answer to THREE decimal places) ______ The hourly cost associated with patient waiting in the coffee shop. (please round your answer to ONE decimal place) ______ The total hourly cost in the coffee shop. (please round your answer to ONE decimal place)
The bank manager is concerned with its waiting line system in his bank. Currently bank uses a single-server, single-line, single-phase system. Based on historical evidence, the average number of customers arriving per hour is C1 and is described by a Poisson distribution. The service rate is <=15 >11 customers per hour with the service times following an exponential distribution. The customers are come from an infinite population. The manager of the bank would like calculate the operational characteristics of the waiting line system that:(a) What is the average system utilization?(b) What is the average number of customers in the system? (c) What is the average number of customers waiting in line?(d) What is the average time a customer spends in the system?(e) What is the average time a customer spends waiting in line?
A community is served by two identical companies providing taxi booking services. Each company owns two cabs, and both book rides at an average rate of eight per hour. The average duration of a ride is 12 minutes meaning each cab makes 5 rides per hour. Calls for booking arrive according to a Poisson distribution, and the rides made is exponential. The two companies have been bought by an investor and will be merged into one. Analyze the new investor's proposal. The following is the queueing model of each company before and after they merge: Company C A = ? rides booked/hr u = ? rides made/hr c = ? cabs Company A Company B A = 8 rides booked/hr µ = 5 rides made/hr 2 cabs A = 8 rides booked/hr µ = 5 rides made/hr = 2 cabs %3D %3D %3D C = с 3 %3D
Find a Doctor is a small startup that helps people find a physician who best meets their needs (location, insurance accepted, etc.). During a “slow” time for it, it has 8 staff members taking calls from customers. On average, one call arrives every 5 minutes (with a standard deviation of 5 minutes). Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27.00 minutes). How long does one of their customers spend, on average, waiting on hold before he or she can start speaking to a representative?
Suppose you’re designing a toll bridge for vehicle traffic over the Cache la Poudre River. Cars are expected to arrive at the central toll plaza at a rate of 400 per hour. You will have five toll booths, which can each process cars at a rate of 120 cars per hour. Assume cars arrive into the toll plaza according to a Poisson distribution with a mean rate of 400 units per period. Assume car processing times are exponentially distributed with a mean service rate of 120 units per period. 1. What is the probability that two channels are busy and no units are waiting in the queue? 2. What is the steady-state average length of the queue (waiting line)? 3. What is the mean number of units in the system (queue and service)?
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
Consider a bank where potential customers arrive at rate of 60 customers per hour. However, because of limited space, one out of every four arriving customers finds the bank full and leaves immediately (without enteringthe bank). Suppose that the average number of customers waiting in line in the bank is 3.5. How long will a typical entering customer have to wait in line? (Hint: In Little’s formula, l refers only to customers who enter the system.)
Car owners fill up when their tanks are exactly half full. At the present time, an average of 8.5 cars/hr arrive at a single-pump gas station. It takes an average of 3.68 minutes to service a car. Suppose that a gas shortage occurs and panic buying takes place. All car owners now purchase gas when their tanks are exactly 3/4 full. Since each car is putting less gas into the tank for each visit, the average service time has been reduced to 2.54 minutes. Assume that arrival and departure rates are both exponential. What is the difference in length of queue before and after the shortage scenario, in terms of vehicles? answer an absolute value, and in four decimal places.
please answer in 30 mins.
Town Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller. 15.What is the average time in minutes that a customer spends in the system? 3.8 mins 7 mins 4.8 mins 8.9 mins
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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