A manual assembly line has six stations. The assembly time at each manual station is 60 sec. Parts are transferred byhand from one station to the next, and the lack of discipline in this method adds 12 sec (Tr = 12 sec) to the cycle time.Hence, the current cycle time is 72 sec. The following two proposals have been made: (1) Install a mechanized transfersystem to pace the line; and (2) automate one or more of the manual stations using robots that would perform the sametasks as humans only faster. The second proposal requires the mechanized transfer system of the first proposal and wouldresult in a partially or fully automated assembly line. The transfer system would have a transfer time of 6 sec, thusreducing the cycle time on the manual line to 66 sec. Regarding the second proposal, all six stations are candidates forautomation. Each automated station would have an assembly time of 30 sec. Thus if all six stations were automated thecycle time for the line would be 36 sec. There are differences in the quality of parts added at the stations; these data aregiven in the accompanying table for each station (q = fraction defect rate, m = probability that a defect will jam thestation). Average downtime per station jam at the automated stations is 3.0 min. Assume that the manual stations do notexperience line stops due to defective components. Cost data: Cat = $0.10/min; Cw = $0.20/min; and Cas = $0.15/min.Station qi mi Station qi mi1 0.005 1.0 4 0.020 1.02 0.010 1.0 5 0.025 1.03 0.015 1.0 6 0.030 1.0Determine if either or both of the proposals should be accepted. If the second proposal is accepted, how many stationsshould be automated and which ones? Use cost per piece as the criterion of your decision. Assume for all cases considered that the line operates without storage buffers, so when an automated station stops, the whole line stops, including themanual stations. (10mks)(c) Solve preceding Problem (b), except that the probability that a defective part will jam the automated station is m = 0.5for all stations. (10mks)