You work for SteelPro a fabrication company that specializes in machining specialty alloys. One of your best customers is Bombardier Transportation. Bombardier has asked you to fill an order for 20 of their part 107. Bombardier will pay you $500 for each good part 107 bu twill only accept exactly 20 good ones- no more, no less. The raw materials required to make a 107 cost $150. Unfortunately, you have yield loss issues related to manufacturing the 107. Assume that the 107s are produced independently of each other with the probability of an individual 107 being good being equal to 0.85. Defective 107s can can be scrapped for $50. There is also the technical challenge that the way you process the 107s is that you machine the entire batch (whatever batch size you choose) and then you heat treat and further process them and only after the heat treating and further processing do the defects become detectable. Thus, you must determine the batch size to run prior to knowing what your precise yield will be. What is the minimum number of 107s you need to schedule to have a 0.90 probability that you get 20 good 107s?