Assignment 2 Problem Set Assignment 1 Problem 4.5 b), c)MAD A.19 F.J. Brewerton Retailers, Inc., must decide whether to build a small or a large facility at a new location in south Texas. Demand at the location will either be low or high, with probabilities 0.4 and 0.6, respectively. If Brewerton builds a small facility and demand proves to be high, he then has the option of expanding the facility. If a small facility is built and demand proves to be high, and then the retailer expands the facility, the payoff is $270,000. If a small facility is built and demand proves to be high, but Brewerton then decides not to expand the facility, the payoff is $223,000. If a small facility is built and demand proves to be low, then there is no option to expand and the payoff is $200,000. If a large facility is built and demand proves to be low, Brewerton then has the option of stimulating demand through local advertising. If he does not exercise this option, then the payoff is $40,000. If he does exer- cise the advertising option, then the response to advertising will either be modest or sizable, with probabilities of 0.3 and 0.7, respec- tively. If the response is modest, the payoff is $20,000. If it is siz- able, the payoff is $220,000. Finally, if a large facility is built and demand proves to be high, then no advertising is needed and the payoff is $800,000 a) What should Brewerton do to maximize his expected payoff? b) What is the value of this expected payoff? $6.7. Auto pistons at Yongpin Zhou's plant in Shanghai are pro- duced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day 1 2 3 4 5 Mean (mm) 156.9 153.2 153.6 155.5 156.6 Range (mm) 4.2 4.6 4.1 5.0 4.5 a. What is the value of ? b. What is the value of ? c. What are the UCL, and LCLX d. What are the UCL R and LCLR e. If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCL; and LCL ? f. Plot the chart for c) and d) 57.15 A production process at Kenneth Day Manufacturing is shown in Figure 57.9. The drilling operation occurs separately from, and simultaneously with the sawing and sanding operations. Assembly Sawing Sanding 0.7 units/hr 6 units/hr 6 units/hr Welding Assembly 0.7 units/hr 2 units/hr Drilling Assembly 2.4 units/hr 0.7 units/hr A FIGURE 57.9 A product needs to go through only one of the three assembly oper ian pizza. Oven type A can hanc ations (the operations are in parallel). associated with oven A are $20, a) Which operation is the bottleneck? per pizza. Oven B is larger and b) What is the process time of the overall system? fixed costs associated with ov c) What is the process cycle time of the overall system? costs are $1.25 per pizza. The p d) If the firm operates 8 hours per day, 20 days per month, what is a) What is the break-even poin the monthly capacity of the manufacturing process? b) If the owner expects to sell