SOLVED

51) 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). Which is cheaper, the existing system with one service crew, or a revised system with two service crews? 52) A dental clinic at which only one dentist works is open only two days a week. During those two days, patients arrive at the rate of three per hour. The doctor serves patients at the rate of one every 15 minutes. a. What is the probability that the clinic is empty (except for the dentist and staff)? b. What percentage of the time is the dentist busy? c. What is the average number of patients in the waiting room? d. What is the average time a patient spends in the office (wait plus service)? e. What is the average time a patient waits for service? 53) A dental clinic at which only one dentist works is open only two days a week. During those two days, the traffic arrivals follow a Poisson distribution with patients arriving at the rate of three per hour. The doctor serves patients at the rate of one every 15 minutes. a. What is the probability that the clinic is empty (except for the dentist and staff)? b. What is the probability that there are one or more patients in the system? c. What is the probability that there are four patients in the system? d. What is the probability that there are four or more patients in the system? 54) At the order fulfillment center of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machine to be sorted for loading onto the appropriate truck for the parcel’s address. The arrival rate at the sorting machine is at the rate of 100 per hour following a Poisson distribution. The machine sorts at the constant rate of 150 per hour. a. What is the utilization rate of the system? b. What is the average number of packages waiting to be sorted? c. What is the average number of packages in the sorting system? d. How long must the average package wait until it gets sorted? e. What would Lq and Wq be if the service rate were exponential, not constant? 55) At the order fulfillment center of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machine to be sorted for loading onto the appropriate truck for the parcel’s address. The arrival rate at the sorting machine is at the rate of 140 per hour following a Poisson distribution. The machine sorts at the constant rate of 150 per hour. a. What is the utilization rate of the system? b. What is the average number of packages waiting to be sorted? c. What is the average number of packages in the sorting system? d. How long must the average package wait until it gets sorted?