Jobs arrive to a two-station serial line at a rate of five jobs per hour with deterministic inter-arrival times. station 1 has one machine, which requires exactly 20 minutes to process a job. station 2 has one machine which requires exactly 15 minutes to process a job, provided it is up, but is subject to failures where the mean time to failure is 9 hours and the mean time to repair is one hour. a) what is the total cycle time at workstation 2 (assume no move batching between two stations)? b) assume we have move batching between two stations. in other words, the second workstation receives batches and puts out individual parts. what is the total cycle time of the system with a batch size k-5? c) how can we improve this system (i. e. how can we reduce ct and wip or increase th)? d) suppose we have moderate variability in workstation 1,le·v-c3 +cf)/2-1. what is the total cycle time in the system with a batch size k=5? e) show that ct increases proportionally with batch size (provide a plot) f) how can we improve this system with moderate variability in workstation 1?