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1. Consider a walk-in dental clinic where patients check in, then see one of two hygienists for cleaning, followed by the dentist. On a busy day, 40 customers get cleaning and a visit by the dentist during the 8 hours of operation. The dentist also serves an average of 12 patients who need other procedures (these patients do not see the hygienist). The 12 patients are not included in the 40 who get both the cleaning and dentist. The average queue sizes are found to be 1.7 for the hygienists and 2.1 for the dentist.What are the average wait times for the hygienists queue and for the dentist queue?
2. Consider a non-profit organization, where grant proposals are written by the business development director. The director, who devotes 100% of his time to the proposals, completes an average of 2.3 per month. On average, 4 RFP’s (requests for proposals) are waiting to be started. What is the average flow time for proposals?
3. A manufacturing work station is preceded by 1600 units of inventory. The workstation's flow rate (i.e., throughput) is 800 units per 8-hour shift. Using Little's Law, calculate the average flow time (in hours) for the work station. A major change of managers and redesign of the workstation is made. As a result, the new flow time is 90 minutes. Assuming that the flow rate remains the same at 800 units per shift, what is the new average inventory level?
4. Consider an oil change facility. The daily throughput averages 75 cars and the facility is opened for 10 hours per day. Three bays operate simultaneously and the average service time per car at each bay is 18 minutes. What is utilization of the bays during a typical day?
5. A very large walk-in hair salon where hair is washed at one of five stations. Currently, customers arrive at the rate of 60 customers per hour and leave the facility at a similar rate. On average, 18 customers are waiting for hair washing. On average, how long do hair washing customers wait (in minutes)? The salon owner believes that many customers are dissatisfied by the long wait and decides to dedicate two of the five stations to short-haired customers and the other three stations to “other” (i.e., medium and long-haired) customers. A study indicates that hair washing takes an average of 3 minutes for each short-haired customers and an average of 6 minutes for “other” customers. As a result of the change, the waiting area has averaged 4 short-haired customers and 6 “other” customers. On average, how long will short-haired customers wait for hair washing (in minutes)? On average, how long will “other” customers wait for hair washing (in minutes)?
6. A manufacturing faculty includes an assembly process, where each product is assembled by one of two assembly workers. Each worker assembles a product in 7.5 minutes. Parts arrive at this department at the rate of 15 parts per hour. Calculate the utilization of the assembly process. If the target utilization were 75% or below, how many assembly workers would be needed?

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