3 25 Soints During the campus Spring Fing, the bumper car amusement attraction has a problem of cars becoming disabled and in need of repair Repair personnel can be hired at the rate of $20 per hour, but they only work as one team. Thus, If one person is hired, he or she works alone; two or three people work together on the same repair One repairer can fx cars in an average time of 45 minutes. Two repairers toke 30 minutes, and three toke 20 minutes. While these cars are down, lost income is 540 per hout Cars tend to break down at the rate of 80 per hour. Management is trying to decide how many repair persons to hire, and has asked you for cost doto. a. What is the total hourly cost with one repair person? (Round your intermediate calculations and final answer to 2 decimal places.) Total cost per hour bo b. What is the total hourly cost with two repair persons? (Round your intermediate calculations and final answer to 2 decimal places.) Total cost per hour c. What is the total hourly cost with three repale persons? (Round your intermediate calculations and final answer to 2 decimal places) Total cost per hour d. How many repairers should be hired? Number of res 4 25 points L Winston Martin (on allergist) has an excellent system for handling his regular patients who come in just for allergy injections. Patients arrive for an injection and fill out a name slip, which is then placed in an open slot that passes into another room staffed by up to three nurses. The specific injections for a patient are prepared, and the patient is called through a speaker system into the room to receive the injection. At certain times during the day. patient load drops and only one nurse is needed to administer the injections Let's focus on the simpler case of the two-namely, when there is one nurse. Also, assume that patients arrive in a Poisson fashion and the service rate of the nurse is exponentially distributed. During this slower period, patients arrive with an interarrival time of approximately 4 minutes. It tokes the nurse an average of 3.20 minutes to prepare the potients' serum and administer the injection Use the Excel spreadsheet Queue Models) a. What is the average number of patients you would expect to see in Dr. Martin's facilities? (Do not round intermediate calculations. Round your answer to 2 decimal places.) 010 Dos Average number of patients Ruferences b. How long would it take for a patient to arrive, get an injection, and leave? (Round your answer to 2 decimal places.) Average total time inues c. What is the probability that there will be three or more patients on the premises? (Do not round intermediate calculations. Round your answer to a decimal place.) Probability What is the utilization of the nurse? (Do not round Intermediate calculations. Round your answer to 1 decimal place.) son of the nurse e. Assume three nurses are available. Each takes an average of 3.20 minutes to prepare the patients' serum and administer the injection. What is the average total time of a patient in the system? (Do not round Intermediate calculations. Round your answer to 2 decimal places.) Agatal time ch Service PE POD 2200 Are A A . 10 S G TO O LO OD OR stor Base 9437 0001 200 13 5 OR SONO 1000 100 OD 0.000 10000 10000 000 10000 Model1 Model 2 Model 2: Single Channel, Poisson Arrival, Constant Service Time Arrival rate 2 = 10 Service rate = 12 Interarrival Time Service time 1/2 = 1/4 = 0.1000 0.0833 System Utilization Average number in line Average number in system Average time in line Average time in system La L. = W,- 0.8333 2.0833 2.9167 0.2083 0.2917 Ws Model 3: Multichannel, Polsson Arrival, Exponential Service Time Arrival Rate 2 100 Service Rate 120 2 3 Number of servers Average number being served Average number in line Average number in system Average time in line Average time in system System Utilization Plzero units in system) Average walting time Pwait) 0.833 0.175 1.008 0.002 0.010 0.417 0.412 0.007 0.245 0.833 0.022 0.856 0.000 0.009 0.278 0.432 0.004 0.058 0.833 0.003 0.836 0.000 0.008 0.208 0.434 0.003 0.011 0.833 0.000 0.834 0.000 0.008 0.167 0.435 0.002 0.002 0.833 0.000 0.833 0.000 0.008 0.139 0.435 0.002 0.000 0.833 0.000 0.833 0.000 0.008 0.119 0.435 0.001 0.000 rho P. W P Nole The la value in Exhibit 10. may differ slightly from the la on this template. The value of Lq in the templates based on a que formula