(1)    Thermostats are subjected to rigorous testing before they are shipped to air conditioning ...

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(1)    Thermostats are subjected to rigorous testing before they are shipped to air conditioning technicians around the world. Results from the last five samples are shown in the table. Is the process under control? Is the process capable of meeting 3 sigma quality performance?                                Unit # Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 1 73.5 70.8 72.2 73.6 71.0 2 71.3 71.0 73.1 72.7 72.2 3 70.0 72.6 71.9 72.4 73.3 4 71.1 70.6 70.3 74.2 73.6 5 70.8 70.7 70.7 73.5 71.1     (2)      The delivery wagon that the hominy man had used for the last three decades was beyond repair, so he decided to open a hominy stand at a busy intersection in downtown Luther. Customers arrive at the rate of 8 per hour and it takes 5 minutes on average to fill their buckets with hominy. What is the likelihood that the line is longer than three people? What is the average waiting time in line? What is the average number of customers in line?     (3)    Boralis manufacture backpacks for hikers. The demand for its products during the peak period of March to June of each year is 100, 200, 180, and 300 units, respectively. The company uses part time labor to accommodate fluctuations in demand. It is estimated that Boralis can produce 50, 180,280, and 270 units in March through June. A current month’s demand can satisfied in one of the three ways. (1)    Current month’s production at the cost of $40 per pack (2)    Surplus production in an earlier monthly at an additional cost of $0.50 per pack per month (3)    Surplus production in a later month (back-ordering) at an additional penalty cost of $2.00 per pack per month.          Boralis wishes to determine the optimal production schedule for the four months (A)   Set up the transportation table (B)   Model for this problem (C)   Use Northwest corner, Least cost and Vogel methods to find the initial feasible solutions (D)   What is the optimum solution