Single server system has customer arrival rate of 60 customers per minute and a service rate of 75 customers per minute. Customer arrival pattern is finite and they won't leave till they are served. The Arrival and Service patterns, both are exponential distribution. Based on the above information calculate a. Server utilization% b. Average numbers of customers in line C. Average time per customer in Line vstem
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- A milling department has 10 machines. Each operates an average of eight hours before requiring adjustment, which takes an average of 3.43 hours. While running, each machine can produce 50 pieces an hour. Use Table 1, Table 2 and Table 3. a. With one adjuster, what is the net average hourly output per machine? (Round your answer to 1 decimal place.) Number of Pieces ?? per machine b. If machine downtime cost is $75 per hour and adjuster cost is $31 per hour, how many adjusters would be optimal? Multiple Choice 1 2 3 4 5Amanda Fall is starting up a new house painting business, Fall Colors. She has been advertisingin the local newspaper for several months. Based on inquiries and informal surveys of the localhousing market, she anticipates that she will get painting jobs at the rate of four per week(Poisson distributed). Amanda has also determined that it will take a four-person team ofpainters an average of 0.7 week (exponentially distributed) for a typical painting job. Determine the number of teams of painters Amanda needs to hire so that customers will have to wait no longer than 2 weeks to get their houses painted.From 3:00 P.M. to 8:00 P.M. the local Big-W Supermarket hasa steady arrival of customers. Customers finish shopping andarrive at the checkout area at the rate of 80 per hour (Poissondistributed). It is assumed that when customers arrive at thecash registers they will divide themselves relatively evenly sothat all the checkout lines are even. The average checkouttime at a register is seven minutes (exponentially distributed).The store manager’s service goal is for customers to be out ofthe store within 12 minutes (on average) after they completetheir shopping and arrive at the cash register. How many cashregisters must the store have open in order to achieve themanager’s service goal?
- 9. Shouldice Hospital in Canada is widely known for one thing—hernia repair! In fact, that is the only operation it performs, and it performs a great many of them. Over the past two decades this small 90-bed hospital has averaged 7,000 operations annually. Last year, it had a record year and performed nearly 7,500 operations. A hernia repair operation at Shouldice Hospital is performed by one of the 12 full-time surgeons assisted by one of seven part-time assistant surgeons. The first operations begin at 7:30 AM each day, Monday through Friday. Surgeons generally take about one hour to prepare for and perform each hernia operation, and they operate on an average of at most four patients per day. This four patient per day limit on the average number of operations performed per surgeon has been found to be the best operating level for the hospital as it takes into account time the surgeons need for patient exams and consultations, updating medical charts, writing reports, traveling to…During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each. Find: (a) The average number of customers waiting for service if 5 clerks are used. (b) The minimum number of clerks needed to keep the average waiting time in the system to under 5 minutes. (c) If clerk cost is $40 per hour and customer waiting time represents a “cost” of $30 per hour, how many clerks can be justified on a cost basis? Please show work.11. Leo manages a receiving station for rice. Farmers deliver their loads of rice from 7 am to 7 pm. Leo can process them at a rate of 4.5 tons an hour, and on a heavy day, a total of 96 tons can be expected. The station has room to hold only 15 tons of rice in inventory prior to processing. Once this space is filled, the farmers’ trucks must wait to dump their contents. What is the throughput (flow) rate after 7 pm (in tons/hr)?
- What are the subcomponents of inconvenience in a customer utility function?a. Location and priceb. Price and volumec. Location and timed. Time and performanceAgan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.9 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. If required, round your answers to four decimal places. Lq = fill in the blank 1 L = fill in the blank 2 Wq = fill in the blank 3 hours W = fill in the blank 4 hours Pw = fill in the blank 5 Service goals dictate that an arriving customer should not wait for service more than an average of 6 minutes. Is this goal being met? If not, what action do you recommend? If the consultant can reduce the average time spent per customer to 8 minutes, what is the mean service rate? If required, round your answer to one…The Universal Manufacturing Company produces a par-ticular product in an assembly-line operation. One of the machines on the line is a drill press that has a single as-sembly line feeding into it. A partially completed unit ar-rives at the press to be worked on every 8 minutes, on average, according to an exponential distribution. Themachine operator can process an average of 10 parts perhour (Poisson distributed). Determine the average numberof parts waiting to be worked on, the percentage of timethe operator is working, and the percentage of time themachine is idle.
- 130) please please help me with this! Owners of a local restaurant are concerned about their ability to provide quality service as they continue to grow and attract more customers. They have collected data from Friday and Saturday nights, their busiest times of the week. During these time periods, about 106 customers arrive per hour for service. Given the number of tables and chairs, and the typical time it takes to serve a customer, the owners estimate they can serve, on average, about 162 customers per hour. Use Exhibit 4.6. Furthermore, the owners anticipate that in one year their demand will double as long as they can provide good service to their customers. a. Currently, during these nights, are they in the zone of service, the critical zone, or the zone of nonservice? EXIBIT IS THE PICTURE ADDED O Critical zone O Zone of service O Zone of nonservice b. Next year, after demand doubles, what must the service capacity increase to (at minimum) to stay out of the critical zone?Note:…Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.6 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer. (a) Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. (Round your answers to four decimal places. Report time in hours.) ?=?=Lq=L=Wq= hW= hPw= (b) Service goals dictate that an arriving customer should not wait for service more than an average of 5 minutes. Is this goal being met? (Round your answer to one decimal place.) Wq (in minutes) = min, which is than the desired wait time, so the goal met. What action do you recommend? (Select all that apply.) Increase the mean service rate.Decrease the mean service rate.There is no need to change the current operating parameters.Hire another…Customers filter into a record shop at an average of 1 per minute (exponential interarrivals) where the service rate is 15 per hour (exponential service times).What is the average number of customers in the system with 8 servers? Question 3 options: 2 3 4 5 6