Green Corporation, located in Guelph, is a world-class designer and diversified manufacturer of precision metallic components and systems for the automotive industry, energy, and mobile industrial markets. The company is a leading-edge supplier of engine, transmission, driveline, modules & systems, and mobile aerial work platforms. Green wants to evaluate the waiting line performance of its production process. Suppose the company hires a service technician to repair machine breakdowns that occur on an average of four per hour, according to a Poisson distribution. The technician can service an average of five machines per hour, following approximately the exponential distribution in service times. The salary and benefits for a worker would be $30 per hour. The company operates 8 hours each day. It has been estimated that the waiting time cost is $50 per hour in the line in terms of lost productivity. a. What is the utilization rate of this service system? b. What is the average time a machine spends in the queue? What is the average downtime for a machine that is broken? How many machines are waiting to be serviced at any given time? c. What is the probability that a zero machine is in the system? What is the probability that there are three or more machines in the system? What is the probability that there are exactly three machines in the system? d. Calculate the total daily waiting cost based on time in the queue. Calculate the total daily service cost. Calculate the total daily cost of the queuing system.