probability

Problem #3 (20 points) - Optimization in Queueing Systems a.) (10 points) A tool crib has exponential interarrival and service times and serves a very large group of mechanics. the mean time between arrivals is 4 minutes. It takes 3 minutes on the average for a tool-crib attendant to service a mechanic. the attendant is paid $10 per hour and the mechanic is paid $15 per hour. Determine the number of the number of attendants that must serve in the system in order to minimize the total cost per hour to the system. b.) (10 points) A tool crib with one attendant serves a group of 10 mechanics. Mechanics work for an exponentially distributed amount of time with a mean of 20 minutes, then go to the crib to request a special tool. Service times by the attendant are exponentially distributed, with a mean of 3 minutes. If the number of attendants can now be changed and if an attendant is paid $6 per hour and a mechanic is paid $10 per hour, determine the number of attendants that should serve in the system in order to minimize the total cost per hour to the system