Please answer all the questions and show your work so I can follow along :)

Question 3: [13pt] Determine the placement of departments for a newly designed facility that will minimize total transportation costs using the data in the following tables. Assume that reverse distances are the same. Use a cost of $5 per trip yard to calculate the minimized total transportation cost. Quality Management [50pt] Question 4: [10pt] Computer upgrades have a nominal time of 80 minutes. Samples of five observations each have been taken, and the results are as listed. Using factors from the following table, determine upper and lower control limits for the mean and range charts, and decide if the process is in control. Question 1: [12pt] An assembly line with 17 tasks is to be balanced. The longest task is 2.4 minutes, and the total time for all tasks is 18 minutes. The line will operate 450 minutes per day. a. [2pt] What are the minimum and maximum cycle times? b. [2pt] What range of output is theoretically possible for the line? c. [2pt] What is the minimum number of workstations needed if the maximum output rate is to be sought? d. [2pt] What cycle time will provide an output rate of 125 units per day? e. [4pt] What output potential will result if the cycle time is (1) 9 minutes? (2) 15 minutes? Question 2: [25pt] A shop works a 400-minute day. The manager of the shop wants an output of 200 units per day for the assembly line that has the elemental tasks shown in the table. Do the following: a. [8pt] Construct the precedence diagram. b. [7pt] Assign tasks according to the most following tasks rule. Break ties with the greatest positional weight rule. c. [7pt] Assign tasks according to the greatest positional weight rule. Break ties with the most following tasks rule. d. Compute the efficiency level for each rule. Which one yields the better set of assignments in this instance? ExtraCredit:? Assume we have 3 locations, A, B, and C, located on the same street. That is, to go from location A to C or to go from location C to A you have to pass through location 2. The distance between locations A and B is 2 miles and the distance between location B and C is 3 miles. We also have 3 departments. Department 1 is responsible of producing raw material, which can then be transferred to Department 2 responsible of processing this material to produce canned food. Canned food is then shipped to Department 3, which serves as a warehouse and distribution center. 1,000 loads are shipped from Department 1 to 2, and 500 loads are shipped from Department 2 to 3 . Location C is the only industrial location, and hence, Department 2 can only be placed at this location. Each truck can take one load at a time, and the same truck can be used to ship loads from one location to another, however, at the end of the day, all trucks need to return to their original location. It costs $20/ mile to move one load. What is the optimal total transportation cost? Question 5: [10pt] Using samples of 200 credit card statements, an auditor found the following: a. [2pt] Determine the fraction defective in each sample. b. [2pt] If the true fraction defective for this process is unknown, what is your estimate of it? c. [2pt] What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for samples of this size? d. [4pt] Is the process in control for 95.4% control level? Question 6: [10pt] The postmaster of a small western town receives a certain number of complaints each day about mail delivery. Determine three-sigma control limits using the following data. Is the process in control? Question 7: [20pt] As part of an insurance company's training program, participants learn how to conduct an analysis of clients' insurability. The goal is to have participants achieve a time in the range of 30 to 45 minutes. Test results for three participants were: Armand, a mean of 38 minutes and a standard deviation of 3 minutes; Jerry, a mean of 37 minutes and a standard deviation of 2.5 minutes; and Melissa a mean of 37.5 minutes and a standard deviation of 1.8 minutes. a. [12pt] Which of the participants would you judge to be capable? Explain. b. [8pt] Can the value of the Cpk? exceed the value of Cp? for a given participant? Explain