Food Goblin Supermarkets use both cashiers and baggers to serve customers at check out. During the peak hours, 8 cashiers and 6 baggers serve approximately 75 customers per hour. On average, a cashier spends 6 minutes at checkout and a bagger spends 4 minutes at bagging to serve a customer. Calculate the utilization of cashiers and their capacity cushion during a peak hour. Calculate the utilization of baggers and their capacity cushion during a peak hour. Calculate the overall average utilization of cashiers and baggers during a peak hour.

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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.

Cakes baked by the Freshfood Bakery are transported from the ovens to be packaged by one of three wrappers. Each wrapper can wrap an average of 200 cakes per hour. The cakes are brought to the wrappers at the rate of 500 per hour. If a cake sits longer than 5 minutes before being wrapped, it will not be fresh enough to meet the bakery’s quality control standards. Does the bakery need to hire another wrapper?

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 5 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 8 vehicles per day with a repair time distribution that approximates a negative exponential distribution.  Assume an 8 hour day. What is the expected average number of snowplows in the garage (waiting for repair and being repaired)? 5 1.04 1.67 8

The VBO grocery store has a checkout counter with a full-time cashier. Customers arrive randomly with an average rate of 20 per hour. The distribution of service time is exponential with an average of 2 minutes. Occasionally, this situation causes a long queue and customer complaints. Since there is no room for another cashier, the manager plans to hire another person to help pack the groceries and reduce the expected service time to 1.5 minutes, still with exponential distribution.  The manager wants the percentage of time when there are more than 2 customers at the cash register to be less than 25%. He also wants no more than 5% of customers to have to wait 5 minutes or more before starting service or 7 minutes or more before finishing service.  a) Use the formulas from the M/M/1 model to calculate L, Lq, W and Wq, π0, π1 and π2 of the current transaction. What is the probability that there are more than 2 customers at the cash register?   (b) Repeat (a) for the helper alternative.

During the evening hours, an average of 52 customers can be found in Sachi’s Sports Bar. About 40 customers arrive each hour. Using Little’s Law, how long does each customer stay at Sachi’s?

Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.P3 = fill in the blank 4 What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.P(More than 2 waiting) = fill in the blank 5 What is the average time a customer waits for service? If required, round your answer to four decimal places.Wq = fill in the blank 6 hours

At the Franklin Post Office, patrons wait in a single line for the first open window. On average, 100 patrons enter the post office per hour, and each window can serve an average of 45 patrons per hour. The post office estimates a cost of $0.10 for each minute a patron waits in line and believes that it costs $20 per hour to keep a window open. Interarrival times and service times are exponential. a. To minimize the total expected hourly cost, how many windows should be open? b. If the post office's goal is to ensure that at most 5% of all patrons will spend more than five minutes in line, how many windows should be open?

A mechanic at the Department of Maintenance makes minor repairs to faulty golf electric carts. The carts break down at an average rate of 4 carts per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 6 carts per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. a- What is the utilization rate for the mechanic?  b- What is the average time in hours that a cart is out of service?