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Queuing Theory

During the "Spring Fling", 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, s/he works alone whereas two or three people would work together on the same broken car.

One repairer can fix one car in an average time of 30 minutes. Two repairers take 20 minutes total per car, and three take a total of 15 minutes per car. There is a lost income of $40 per broken car per hour. Cars break down at an average rate of two per hour. Assume all rates are Exponential.