HAL Computer has a printed-circuit board plant that contains a line with two stations. The first station (resist apply) applies a photoresist material to circuit boards. The second station (expose) exposes the boards to ultraviolet light to produce a circuit pattern that is later etched onto the boards. Because the expose operation must take place in a clean room, space for WIP between the two processes is limited to 20 jobs. Capacity calculations show the bottleneck to be expose, which requires an average of 22 minutes to process a job, with an SCV of one. Resist apply requires 19 minutes per job, with an SCV of 0.25 . In addition (and not included in the above process times), expose has a mean time to failure (MTTF) of 331 hours and a mean time to repair (MTTR) of 10 minutes, while resist apply has an MTTF of 48 hours and an MTTR of 8 hours. Jobs arrive to resist apply with a fair amount of variability, so we assume an arrival SCV ca2 of one. The desired throughput rate is 2.4 jobs per hour. Also assume cr=1 as well. From past experience, HAL knows the line to be incapable of achieving the target throughput. To remedy this situation, the responsible engineers are in favour of installing a second expose machine. However, in addition to being expensive, a second machine would require expanding the clean room, which would add significantly to the cost and would result in substantial lost production during construction. The challenge, therefore, is to use our knowledge to find a better solution. Problem\#1 (50 Points) If you recall in class, we calculated step by step that at 2.4job/hr arrival rate, CTq at first station is 645 minutes, average WIP is 25.8 jobs. In this homework, I would like to ask you to calculate step by step that the CTq at second station is 892 minutes, average WIP is 35.7 jobs. Problem\#2 (50 Points) If this printed-circuit board plant applies the machine learning algorithms we developed in the lab sessions. It helps to identify the machine failures ahead of time so that no machine failure will happen during operations at station 1 . Under this condition, what is the expected WIP levels at station 2. What is the percentage reduction in WIP compared with the cases without applying our machine learning algorithms