1. In a production run of 300 units, there are exactly 20 defective items and 280 good items.
(a) What is the probability that a randomly selected item is defective?
(b) If two items are sampled without replacement, what is the probability that both are good?
(c) If two items are randomly sampled without replacement, what is the probability that the first is good but the second is defective?
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2. An urn contains 7 blue and 3 yellow chips. If the drawing of chips is done with replacement, determine the probability of:
(a) Drawing three yellow chips.
(b) Drawing a blue chip on the first draw and a yellow chip on the second draw.
(c) Drawing a blue chip on the second draw given that a yellow chip was drawn on the first draw.
(d) Drawing a yellow chip on the second draw given that a blue chip was drawn on the first draw.
(e) Drawing a yellow chip on the second draw given that a yellow chip was drawn on the first draw.
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3. The decomposition approach to forecasting (using trend and seasonal components) may be helpful when attempting to forecast a time-series. Could an analogous approach be used in a multiple regression analysis? Explain briefly.
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4. Explain the purpose of the ABC analysis and describe the steps needed to perform one.
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5. Four projects must be completed, and each of four employees will be assigned to work on exactly one of the four projects. The table below presents an estimate of the cost that each employee would incur if working on the respective projects. What is the minimum-
cost assignment of workers to projects?
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6. A bakery produces muffins and doughnuts. Let x1 be the number of doughnuts produced and x2 be the number of muffins produced.
The profit function for the bakery is expressed by the following equation: profit = 4×1 + 2×2 + 0.3×12 + 0.4×22.
The bakery has the capacity to produce 800 units of muffins and doughnuts combined and it takes 30 minutes to produce 100 muffins and 20 minutes to produce 100 doughnuts. There is a total of 4 hours available for baking time. There must be at least 200 units of muffins and at least 200 units of doughnuts produced. Formulate a nonlinear program representing the profit maximization problem for the bakery.
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7. Peruse through the various queuing theory models; choose one model, describe its characteristics, and how it applies to the overall systemic function.
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8. Compare and contrast the differences between single-channel queuing systems and multichannel queuing systems. Describe your answer in full.
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Course Textbook
Render, B., Stair, R. M., Jr., & Hanna, M. E. (2012). Quantitative analysis for management (11th ed.). Upper Saddle River, NJ: Prentice Hall.
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