Question 6.1 An analyst has drawn twelve samples, each containing six sample points, from a process that produces a product. The diameter of each product in the samples was determined. The results were tabulated and sample means and ranges were computed. The results were: Sample Sample Mean (in.) 10.012 10.007 9.991 10.006 9.997 9.999 10.001 10.005 9.995 10.001 10.003 Range (in.) 0.009 0.014 0.007 0.026 0.016 0.012 0.008 0.013 0.015 0.011 0.014 8 9 10 11 BUSI 2113 PRODUCTION AND OPERATIONS MANAGEMENT 5 YORKVILLE UNESTY WWW.YORKVILLEU.CA 12 10.006 0.009 a) Determine the upper and lower control limits and the overall means for x-charts and R-charts. b) Draw the charts and plot the values of the sample means and ranges. c) Do the data indicate a process that is in control? d) Why or why not? Question 6.2 A manufacturer produces three types of humidifiers. The retail price of Humidifier Regular (HR) is $60 with variable costs of $20. Humidifier Advanced (HA) sells for $200 for its advanced features. This model's variable costs are $80. Humidifier Simple (HS) is a simplified version and only sells for $25 with variable costs of $15. The manufacturer has machines and facilities worth $320,000 annually. The sales data show that 1000 units of HR, 2000 units of HA, and 10,000 units of HS was sold last year. Calculate the break-even point of the firm. The firm has some idle capacity at these volumes, and chooses to cut the selling price of HR from $60 to $45, believing that its sales volume will rise from 1000 units to 2500 units. What is the revised break-even point? Question 6.3 Leonard's company purchases a window hardware from William's Hardware Co and sells to the market. Leonard is also considering manufacturing the product internally. William's Hardware Co. charges $4 per unit, with a minimum order of 3,000 units. If Leonard manufactures the product in- home, the process setup fee could be $15,000 and then $1.82 per unit for labor and materials. a) Draw a graph illustrating the crossover (or indifference) point. b) Determine the number of units where either choice has the same cost