For all the problems to receive full scores you have to show your complete and accurate work. If you only provide the final answers without showing your computations you will not be assigned a full score (or you will miss the opportunity of receiving partial credit).Problem 1: Line Balancing (9 points)Employees at ABC Assembly Line work from 6am to 2pm Monday through Friday. Everyone on the assembly line is allowed a 30 minute lunch and two 15 minute breaks. Other cross-trained associates cover lunches and breaks for the associates on the assembly line so the line doesn t stop. On your second week at ABC Assembly Line you record the processes of the assembly line are laid out in the following manner:Task Predecessor 1 none 2 1 3 none 4 2 5 3 6 4 5The intern the summer before recorded the following observations:Task 1 average cycle time = 1.1 minTask 2 average cycle time = 0.8 minTask 5 average cycle time = 1.4 minYou complete the 20 observations at each of the other 3 stations and record the following:Task 3 average cycle time = 52 secTask 4 average cycle time = 36 secTask 6 average cycle time = 63 secDue to quality issues in the field causing $300k worth of parts to be recalled a new quality check Task 4a needs to be added after Task 4 and the quality check must be completed before Task 6 can begin. The Quality Assurance Team estimates this new process will take an average of 27 seconds to complete. Prior to adding this quality check task the line was achieving an output of 300 units per day and the Plant Manager needs to maintain that output.Assuming the new quality check task is added do the following:a)Draw the precedence diagram with the processing times for each task displayed (2 points).b)Compute the Takt time for the line (1 point).c)Assign tasks to work stations using the greatest amount of time remaining as a heuristic rule (2 points).d)Compute the efficiency and percent idle time for the system (2 points).e)Determine which work station has the least amount of idle time (1 point). Determine which work station has the greatest amount of idle time (1 point).

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