3. A manufacturing cell has 4 operators (working independently in parallel) and a shared buffer space that can fit at most 6 incoming jobs. During a production period, jobs arrive to the cell with rate of 10 jobs per hour (Poisson arrival, i.e., exponential inter-arrival time). The average processing time of a job is 30 minutes (exponentially distributed service time). Answer the following questions using the analytical formulas learned in class. (a) Explain why the M/M/4/10 queueing model should be used to model this problem. (b) Show that the long-term average waiting time of a job in the buffer is 0.4554 hr or 27.3 min. (c) Show that the probability that an arriving job cannot be admitted into the cell due to full occupancy is 0.2301.