Question 4: A maintenance worker repairs machines that break down at an average rate of 4 per hour. The breakdown follows Poisson distribution. The time to repair a machine follows exponential distribution with a mean of 12 minutes. The maintenance worker is paid $9 per hour. It is estimated that the cost of machine waiting time in line is $ 3 per hour. A) Determine the proportion of time that the maintenance worker is busy B) What is the average number of machines in the queue C) What fraction of time do you expect to have more than three machines in the system D) How long will the machine have to wait before serving by the maintenance worker E) Assume that another maintenance worker has been interviewed. He demands $12 per hour and services at an average rate of 7 machines per hour. Show the cost analysis. Which repairman would you recommend and why?

Question 4: A maintenance worker repairs machines that break down at an average rate of 4 per hour. The breakdown follows Poisson distribution. The time to repair a machine follows exponential distribution with a mean of 12 minutes. The maintenance worker is paid $9 per hour. It is estimated that the cost of machine waiting time in line is $ 3 per hour. A) Determine the proportion of time that the maintenance worker is busy B) What is the average number of machines in the queue C) What fraction of time do you expect to have more than three machines in the system D) How long will the machine have to wait before serving by the maintenance worker E) Assume that another maintenance worker has been interviewed. He demands $12 per hour and services at an average rate of 7 machines per hour. Show the cost analysis. Which repairman would you recommend and why