4. For each of the accompanying control charts, analyze the data using both median and up/down run tests with z = 1.96 limits. a.Are nonrandom variations present? Assume the center line is the long-term median. Picture Test Conclusion Median Up/Down b.Are nonrandom variations present? Assume the center line is the long-term median. Picture Test Conclusion Median Up/Down 5. A company has just negotiated a contract to produce a part for another firm. In the process of manufacturing the part, the inside diameter of successive parts becomes smaller and smaller as the cutting tool wears. However, the specs are so wide relative to machine capabilities that it is possible to set the diameter initially at a large value and let the process run for a while before replacing the cutting tool. The inside diameter decreases at an average rate of .001 cm per part, and the process has a standard deviation of .05 cm. The variability is approximately normal. Assuming a three-sigma buffer at each end, how frequently must the tool be replaced if the process specs are 3 cm and 3.5 cm. Use (Number of shafts) n = 1.Picture Determine how many pieces can be produced before the LCL just crosses the lower tolerance of 3 cm. (Do not round your intermediate calculations.) After pieces the cutting tool should be replaced. 6. A production process consists of a three-step operation. The scrap rate is 10 percent for the first step and 6 percent for the other two steps. a.If the desired daily output is 450 units, how many units must be started to allow for loss due to scrap? (Do not round intermediate calculations. Round up your final answer to the next whole number.) Number of units b.If the scrap rate for each step could be cut in half at every operation, how many units would this save in terms of the scrap allowance? (Do not round intermediate calculations. Round up your final answer to the next whole number.) Number of units c.If the scrap represents a cost of $10 per unit, how much is it costing the company per day for the original scrap rate (i.e. the Part a scrap rate)? (Round your answer to the nearest whole number. Omit the “$” sign in your response.) Cost$ 12. Use the assignment method to obtain a plan that will minimize the processing costs in the following table under these conditions: WORKER ABCDE 11418201718 21415191617Job31216151417 41113141214 51016151413 a.The combination 2-D is undesirable. The sequence is. b.The combinations 1-A and 2-D are undesirable. The sequence is . The following table shows orders to be processed at a machine shop as of 8:00 a.m. Monday. The jobs have different operations they must go through. Processing times are in days. Jobs are listed in order of arrival. JobProcessingTime (Days)Due Date(Days)Remaining Numberof OperationsA8 202B10 184C5 255D11 173E9 354 a.Determine the processing sequence at the first work center using each of these rules: (1) First come, first served, (2) Slack per operation. Sequence for First come, first served Sequence for Slack per operation b.Compute the effectiveness of each rule using each of these measures: (1) average completion time, (2) average number of jobs at the work center. (Round your answers to 2 decimal places.) First Come, First ServedSlack per Operation Average completion time Average number of jobs 14. The times required to complete each of eight jobs in a two-machine flow shop are shown in the table that follows. Each job must follow the same sequence, beginning with machine A and moving to machine B. TIME (hours)JobMachine AMachine Ba16 5 b3 13 c9 6 d8 7 e2 14 f12 4 g18 14 h20 11 a.Determine a sequence that will minimize makespan time. The sequence is. b.Find machine Bs idle time. Idle timehrs c.For the sequence determined in part a, how much would machine B’s idle time be reduced by splitting the last two jobs in half? 16. For each of the following network diagrams, determine both the critical path and the expected project duration. The numbers on the arrows represent expected activity times. a.Activity-on-arrow diagram Picture The critical path is. The expected project duration is . b.Activity-on-node diagram Picture The critical path is. The expected project duration is . c.Activity-on-arrow diagram Picture The critical path is. The expected project duration is . 17. For each of the problems listed, determine the following quantities for each activity: the earliest start time, latest start time, earliest finish time, latest finish time, and slack time. List the critical activities, and determine the expected duration of the project. a. Activity-on-arrow diagram Picture Summary: Activity ES EF LF LS Slack 12 24 47 710 1012 25 58 810 13 36 69 911 1112 b. Activity-on-node diagram Picture Summary: Activity ES EF LF LS Slack1 2 3 4 5 6 7 8 9 c. ActivityImmediatePredecessorEstimated Time (days)A15 BA12 CB6 DB5 EC3 F8 GF8 HF9 IG7 JH14 KJ6 EndD, E, I, K Summary: Activity ES EF LF LS SlackA B C E D F G I H J K 18. Reconsider the network diagram. Suppose that after 12 weeks, activities 1-2, 1-3, and 2-4 have been finished; activity 2-5 is 75 percent finished; and activity 3-6 is half finished. How many weeks after the original start time should the project be finished?Picture Project can be completed in a total of weeks. 4. For each of the accompanying control charts, analyze the data using both median and up/down run tests with z = 1.96 limits. a.Are nonrandom variations present? Assume the center line is the long-term median. Picture Test Conclusion Median Up/Down b.Are nonrandom variations present? Assume the center line is the long-term median. Picture Test Conclusion Median Up/Down 5. A company has just negotiated a contract to produce a part for another firm. In the process of manufacturing the part, the inside diameter of successive parts becomes smaller and smaller as the cutting tool wears. However, the specs are so wide relative to machine capabilities that it is possible to set the diameter initially at a large value and let the process run for a while before replacing the cutting tool. The inside diameter decreases at an average rate of .001 cm per part, and the process has a standard deviation of .05 cm. The variability is approximately normal. Assuming a three-sigma buffer at each end, how frequently must the tool be replaced if the process specs are 3 cm and 3.5 cm. Use (Number of shafts) n = 1.Picture Determine how many pieces can be produced before the LCL just crosses the lower tolerance of 3 cm. (Do not round your intermediate calculations.) After pieces the cutting tool should be replaced. 6. A production process consists of a three-step operation. The scrap rate is 10 percent for the first step and 6 percent for the other two steps. a.If the desired daily output is 450 units, how many units must be started to allow for loss due to scrap? (Do not round intermediate calculations. Round up your final answer to the next whole number.) Number of units b.If the scrap rate for each step could be cut in half at every operation, how many units would this save in terms of the scrap allowance? (Do not round intermediate calculations. Round up your final answer to the next whole number.) Number of units c.If the scrap represents a cost of $10 per unit, how much is it costing the company per day for the original scrap rate (i.e. the Part a scrap rate)? (Round your answer to the nearest whole number. Omit the “$” sign in your response.) Cost$ 12. Use the assignment method to obtain a plan that will minimize the processing costs in the following table under these conditions: WORKER ABCDE 11418201718 21415191617Job31216151417 41113141214 51016151413 a.The combination 2-D is undesirable. The sequence is. b.The combinations 1-A and 2-D are undesirable. The sequence is . The following table shows orders to be processed at a machine shop as of 8:00 a.m. Monday. The jobs have different operations they must go through. Processing times are in days. Jobs are listed in order of arrival. JobProcessingTime (Days)Due Date(Days)Remaining Numberof OperationsA8 202B10 184C5 255D11 173E9 354 a.Determine the processing sequence at the first work center using each of these rules: (1) First come, first served, (2) Slack per operation. Sequence for First come, first served Sequence for Slack per operation b.Compute the effectiveness of each rule using each of these measures: (1) average completion time, (2) average number of jobs at the work center. (Round your answers to 2 decimal places.) First Come, First ServedSlack per Operation Average completion time Average number of jobs 14. The times required to complete each of eight jobs in a two-machine flow shop are shown in the table that follows. Each job must follow the same sequence, beginning with machine A and moving to machine B. TIME (hours)JobMachine AMachine Ba16 5 b3 13 c9 6 d8 7 e2 14 f12 4 g18 14 h20 11 a.Determine a sequence that will minimize makespan time. The sequence is. b.Find machine Bs idle time. Idle timehrs c.For the sequence determined in part a, how much would machine B’s idle time be reduced by splitting the last two jobs in half? 16. For each of the following network diagrams, determine both the critical path and the expected project duration. The numbers on the arrows represent expected activity times. a.Activity-on-arrow diagram Picture The critical path is. The expected project duration is . b.Activity-on-node diagram Picture The critical path is. The expected project duration is . c.Activity-on-arrow diagram Picture The critical path is. The expected project duration is . 17. For each of the problems listed, determine the following quantities for each activity: the earliest start time, latest start time, earliest finish time, latest finish time, and slack time. List the critical activities, and determine the expected duration of the project. a. Activity-on-arrow diagram Picture Summary: Activity ES EF LF LS Slack 12 24 47 710 1012 25 58 810 13 36 69 911 1112 b. Activity-on-node diagram Picture Summary: Activity ES EF LF LS Slack1 2 3 4 5 6 7 8 9 c. ActivityImmediatePredecessorEstimated Time (days)A15 BA12 CB6 DB5 EC3 F8 GF8 HF9 IG7 JH14 KJ6 EndD, E, I, K Summary: Activity ES EF LF LS SlackA B C E D F G I H J K 18. Reconsider the network diagram. Suppose that after 12 weeks, activities 1-2, 1-3, and 2-4 have been finished; activity 2-5 is 75 percent finished; and activity 3-6 is half finished. How many weeks after the original start time should the project be finished?Picture Project can be completed in a total of weeks.