2. The annual demand for Lipiprozac, a wonder drug, is normally distributed with mean 40,000 and standard deviation 5,000. There is evidence that the maximum and minimum annual demands are 52,000 and 21,000, respectively. Assume that demand during each of the next 10 years is an independent random draw from this distribution. The company producing Lipiprozac needs to determine how large a manufacturing plant to build to maximize its expected profit over the next 10 years. If the company build a plant that can produce x units of the drug per year, it will cost $18 for each of these units. The company will produce only the amount demanded each year, and each unit of Lipiprozac produce will sell for 51.25. Each unit of Lipiprozac produced incurs a variable production cost of $0.35. The cost per year to operate a unit of capacity follows a triangular distribution with the following parameters (in dollars): 0.28, 0.38, and 0.48. It has been found that this last cost and the annual demand has a correlation of 0.86.a. Using simulation, among the capacity levels of 20,000, 30,000, 40,000, 50,000, and 60,000 units per year, which level maximizes expected profit?b. Using the capacity from you answer to part a, the company can be 95% certain the expected profit for the 10-year period will be between what two values?c. Using the capacity from you answer to part a, the company cab be 90% certain the actual profit for the 10-year period will be between what two values?

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