Food Goblin Supermarkets use both cashiers and baggers to serve customers at check out. During the first 7 hours of each workday (Monday-Friday), 6 cashiers and 2 baggers serve approximately 25 customers per hour. A cashier and a bagger who require approximately 6 minutes at checkout and 4 minutes at bagging serve each customer. a. The utilization of cashiers is 41.7%. (Enter your response rounded to one decimal place.) The utilization of baggers is %. (Enter your response rounded to one decimal place.)

A study-aid desk staffed by a graduate student has been established to answer students' questions and help in working problems in your OSCM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of four per hour and the distribution is approximately Poisson. Assistance time averages 10 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS. Calculate the percentage utilization of the graduate student. Note: Round your answer to 1 decimal place.   Calculate the average number of students in the system, including the graduate student service desk. Note: Round your answer to the nearest whole number.   Calculate the average time in the system. Note: Round your answer to the nearest whole number.   Calculate the probability of four or more students being in line or being served. Note: Round your intermediate calculations to 3…

4.) The DMV Licensing office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. a.) What percentage of the total available service time is being used? b.) Due to Covid restrictions, only two customers are allowed in the office at the same time. What percent of the time will there be customers waiting outside?

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You have started a new business with your friends while you are still a student. You have special clientele.. they like snakes as pets…Hence you start a tea/snake shop (you will serve tea and snakes for entertaining your clients). You decide to hire one server in the beginning. You expect about 15 customers per hour (mean value with Poission distributed arrivals) arriving in the morning hours. The server will take about 4 minutes to serve a customer (mean time). For this situation (Situation A) Find: a. Arrival and service rates b. Find system utilization c. Percentage of time server is idle d. What is wrong with the picture? e. What can you do to help the situation? f. Once you correct the situation (adopt one of the possible solutions), find probability of 5 customers in the system. g. Find the expected number of customers waiting to be served. h. What is the service and weight times (system wait time)? i. Solve the above problem assuming M/M/1 queue discipline. You are now become…

3 The M/M/1 Queue During peak time, customers arrive at a bank teller window (with a single teller) at a rate of 23 per hour, where the teller can serve 25 per hour. This problem will allow you to investigate (via a simple extension of the mean queue size formula) the effect of highly-variable service times on our familiar queuing metrics. The diagram below stylizes the queuing system: Waiting Service Calculate the marginal probability P (T > oT). a. O b. 0.25 O c. 0.63 O d. 0.75 Calculate the mean time a customer spends at the bank (waiting time plus service time) in minutes. O a. 30 minutes O b. 27.6 minutes O c. 2.4 minutes O d. 7 minutes