Students arrive at the cafeteria every 2.5 minutes on average.The average of 15 students’ orders per hour can be processed.The cafeteria is staffed by two workers. Assume Poisson arrivaland exponential service time situation. The cafeteria opens 10hours per day. If each student's waiting cost is $7 per hour andhiring cost to hire another worker is $20 per hour (the sameservice rate), should another worker be hired? Northeast Pennsylvania Manufacturing Company haspurchased a certain component part from Wilkes PartCompany for $80 per part. Recently, improvements inoperations and reduce product demand have cleared upinsomeсарacityNortheastPennsylvaniaManufacturing's own plant for producing componentparts. The particular part could be produced at $50 perpart, with a fixed cost of $200,000. As anotheralternative, a new supplier, Scranton Part Company, isoffering volume discounts for new customers of $90 perpart for the first 1,600 parts ordered and $70 per part foreach additional unit ordered. At what volume wouldeach of the alternatives be preferred?

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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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Below are the data of the gasoline station. Number of gas pumps = 1 Policy of the gasoline station is "If you want to wait, pay PhP45 per liter; if you do't want to wait, pay PhP55/liter." Service mean time (exponential distribution) = 5 minutes Arrival rate (Poisson distribution) = 10 per hour. Customers usually wait to buy gasoline. a) What is the probability (in decimal) that customer will wait? Answer in 4 decimal places.b) Determine the probability that the customer will not wait. Answer in 4 decimal places.c) How many customers are falling in line? Answer in integer value.d) Determine the expected price of gasoline per liter.
For the first three minutes of the day, the arrival rate at the book store is 23 customers per minute. The book store is capable of serving 21 customers per minute. Assume that the system is empty at the start and that no customer who arrives leaves without being served. (Round your answer to 2 decimal places.) What is the average wait time for customers during this time period (in minutes)? minute
[Queuing Theory - Operation research] The take-out counter at an ice-cream parlor is serviced by one attendant. Customers arrive according to a Poisson process, at a mean arrival rate of 30 per hour. They are serviced on a FCFS basis, and because of the quality of the ice cream, they are willing to wait if necessary. The service time per customer appears to be exponentially distributed, with a mean of 1.5 minutes. Determine the following: (a) probability that the system is idle (b) average number of customers in the system (c) amount of time a customer should expect to wait before service (d) probability that a customer will have to spend more than 15 minutes in the queue
Students arrive at the Administrative Services Office at an average of one every 6 minutes, and their requests take, on average, 4 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. a. What percentage of time is Judy idle? (Round your answer to 1 decimal place.) b. How much time, on average, does a student spend waiting in line? (Do not round intermediate calculations. Round your answer to 1 decimal place.) c. How long is the (waiting) line on average? (Round your answer to 2 decimal places.) d. 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? (Do not round intermediate calculations. Round your answer to 4 decimal places.)
There is only one copying machine in the student lounge of the business school. Students arrive at the rate of λ=40 per hour (according to a Poisson distribution). Copying takes an average of 40 seconds, or μ=90 per hour (according to a negative exponential distribution). If the percentage of time used is 44% and the average length of the queue is 35 students and the average number is 80 then what is the average time spent waiting in the queue and the average time in the system (round your response to two decimal points).
A Northwest Airlines ticket counter forecasts that 30 people per hour will need to check in. It takes an average of 1.5 minutes to service a customer. Assume that interarrival times and service times are exponential and that all customers wait in a single line for the first avaliable agent.If we want the average time a customer spends in line and in service to be 3 minutes or less, how many ticket agents should be on duty?
Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.c. How many customers are in the bakery on average?
Customers arrive randomly to an airport shoe-shine stand with only ONE attendant at a rate of 8 per hour. The average length of a shoe shine is 12 minutes. Assume that service times are exponentially distributed and that the queuing system model is (M/M/1):(GD/infinity/infinity). Does this queuing system have a steady state? It cannot be determined. Yes none of the other choices No
What problems would a company experience in relocating its executives from a heavily populated industrialized area to a small rural town?
Josh’s Hot Dogs is a one-person hot dog stand, and normally gets about 14 customers per hour. Assuming that Josh can serve one customer in about 3 minutes. What impact does this have on the queuing characteristics? Specifically, the following questions:a. Mean number of customer in the queue b. Mean number of customer in the system: c. Mean waiting time in the queue:d. Mean waiting time in the system:e. Utilization factor for the system:f. Probability of more than 1 customer in the system at any given time.g. Do you think he has an acceptable queuing system?
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
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

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