SOLVED

46) A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 7.5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 10 vehicles per day with a repair time distribution that approximates an exponential distribution. a. What is the utilization rate for this service system? b. What is the average time before the facility can return a breakdown to service? c. How much of that time is spent waiting for service? d. How many vehicles are likely to be in the system at any one time? 47) A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 7 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ= 11 vehicles per day with a repair time distribution that approximates an exponential distribution. a. What is the utilization rate for this service system? b. What is the average time before the facility can return a breakdown to service? c. How much of that time is spent waiting for service? d. How many vehicles are likely to be waiting for service at any one time? 48) A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ= 10 vehicles per day with a repair time distribution that approximates an exponential distribution. a. What is the probability that the system is empty? b. What is the probability that there is precisely one vehicle in the system? c. What is the probability that there is more than one vehicle in the system? d. What is the probability of 5 or more vehicles in the system? 49) A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 8 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ= 11 vehicles per day with a repair time distribution that approximates an exponential distribution. The crew cost is approximately $300 per day. The cost associated with lost productivity from the breakdown is estimated at $150 per vehicle per day (or any fraction thereof). What is the expected cost of this system? 50) A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 8 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ= 10 vehicles per day with a repair time distribution that approximates an exponential distribution. a. What is the probability that the system is empty? b. What is the probability that there is precisely one vehicle in the system? c. What is the probability that there is more than one vehicle in the system? d. What is the probability of 5 or more vehicles in the system? (a) P0 = 1 – 8/10 = 0.20; (b) Pn > 1 =(8/10)2 = 0.64; the probability of exactly one is 1 – .64 -.20 = .16; (c) 0.64 as previously calculated; (d) Pn > 4 = (8/10)5 = 0.32768