Consider the following 3-station serial production line: • Station 1 has 5 identical machines with average processing time of 15 min per job. • Station 2 has 12 identical machines with average processing times of 30 min per job. • Station 3 has one machine with average processing time of 3 min per job. a) (6 pts) What are the bottleneck rate, the raw process time and the critical WIP? b) (7 pts) Compute the average cycle time when the inventory level is set at 20 jobs, under the assumptions of i) the best case, ii) the worst case and iii) the practical worst case. c) (7 pts) Suppose you want the throughput of the line to be 90% of the bottleneck rate. Find the WIP level required to achieve this under the assumptions of i) the best case, ii) the worst case and iii) the practical worst case. d) (5 pts) If the cycle time at the critical WIP is 100 minutes, where does performance fall relative to the three cases? Is there much room for improvement?