During the campus 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. One repairer can fix cars in an average time of 25 minutes. While a car is disabled or being repaired, lost income is $40 per hour. Cars tend to break down at the rate of two per hour. Assume that there is only one repair person, the arrival rate follows a Poisson distribution and the service time follows an exponential distribution.
a) On average, how long is a disabled bumper car waiting to be serviced?
b) On average, how many disabled bumper cars are out of service waiting to be serviced or being serviced?
c) When a bumper car becomes disabled, what is the probability that it will find that there are at least three cars already waiting to be repaired?
d) The amusement part has decided to increase its repair capacity by adding either one or two additional repair people. These will not work individually but they only work as one team. Thus if two or three people are working, they will work together on the same repair. One repair worker can fix cars in an average time of 25 minutes. Two repair workers working as a team take 20 minutes and three repair workers working as a team take 15 minutes. What is the cost of the repair operation for the two repair strategies (adding 1 or 2 repair workers) that it is considering?
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