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business
an introduction to management science

Questions and Answers of An Introduction to Management Science

=Ad. Use TreePlan to construct and solve this new decision tree.
=A9.15. Reconsider Problem 9.14. Max is skeptical that his estimates (60 percent and 20 percent) could be so far off the percentages (80 percent and 40 percent) obtained by Jennifer, so he requests
=a. Use the spreadsheet shown in Figure 9.18 (available in one of this chapter’s Excel files) to obtain the results when Jennifer’s probabilities are used.
=b. Use SensIt to generate two graphs like Figure 9.20 where the horizontal axis for one is the probability in cell W33, P(FSS|Oil), and the horizontal axis for the other is the probability in cell
=c. Generate the spider graph and tornado diagram when Jennifer’s probabilities are used instead of Max’s estimates.
=9.17.* Vincent Cuomo is the credit manager for the Fine Fabrics Mill. He is currently faced with the question of whether to extend$100,000 of credit to a potential new customer, a dress
=a. Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table when the credit-rating organization is not used.
=b. Assuming the credit-rating organization is not used, use Bayes’ decision rule to determine which decision alternative should be chosen.
=Ac. Find the expected value of perfect information. Does this answer indicate that consideration should be given to using the credit-rating organization?
=d. Assume now that the credit-rating organization is used. Develop a probability tree diagram to find the posterior probabilities of the respective states of nature for each of the three possible
=Te. Use the corresponding Excel template to obtain the answers for part d.
=f. Draw the decision tree for this entire problem by hand. Use this decision tree to determine Vincent’s optimal policy.
=A g. Use TreePlan to construct and solve this decision tree.
=A h. Find the expected value of sample information. If the fee for using the credit-rating organization is open to negotiation, how large can the fee be and use of this organization still be
=9.18. You are given the following payoff table (in units of dollars):State of Nature Alternative S1 S2 A1 400 100 A1 0 100 Prior probability 0.4 0.6 You have the option of paying $100 to have
=9.19. An athletic league does drug testing of its athletes, 10 percent of whom use drugs. The test, however, is only 95 percent reliable. That is, a drug user will test positive with probability
=9.20. Management of the Telemore Company is considering developing and marketing a new product. It is estimated to be twice as likely that the product would prove to be successful as unsuccessful.
=c. Find the expected value of perfect information. Does this answer indicate that consideration should be given to conducting the market survey?
=Td. Assume now that the market survey is conducted.Find the posterior probabilities of the respective states of nature for each of the two possible predictions from the market survey.
=Ae. Use TreePlan to construct and solve the decision tree for this entire problem.
=Af. Use SensIt to generate a spider chart and tornado chart with respect to the profit, loss, and cost data when each can vary as much as 25 percent in either direction from its base value.
=9.21. The Hit-and-Miss Manufacturing Company produces items that have a probability p of being defective. These items are produced in lots of 150. Past experience indicates that p for an entire lot
=a. Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table if the single item is not inspected in advance.
=b. Assuming the single item is not inspected in advance, use Bayes’ decision rule to determine which decision alternative should be chosen.
=c. Find the expected value of perfect information. Does this answer indicate that consideration should be given to inspecting the single item in advance?
=Td. Assume now that the single item is inspected in advance. Find the posterior probabilities of the respective states of nature for each of the two possible outcomes of this inspection.
=Ae. Construct and solve the decision tree for this entire problem.Af. Find the expected value of sample information. If the
=cost of using the laboratory to inspect the single item in advance is open to negotiation, how large can the cost of using the laboratory be and still be worthwhile?
=9.22.* Silicon Dynamics has developed a new computer chip that will enable it to begin producing and marketing a personal computer if it so desires. Alternatively, it can sell the rights to the
=9.23.* Reconsider Problem 9.22. Management of Silicon Dynamics now is considering doing full-fledged market research at an estimated cost of $1 million to predict which of the two levels of demand
=a. Find the expected value of perfect information for this problem.
=b. Does the answer in part a indicate that it might be worthwhile to perform this market research?c. Develop a probability tree diagram to obtain the posterior probabilities of the two levels of
=Td. Use the corresponding Excel template to check your answers in part c.
=A9.24.*Reconsider Problem 9.23. The management of Silicon Dynamics now wants to see a decision tree displaying the entire problem.a. Use TreePlan to construct and solve this decision tree.
=b. Find the expected value of sample information. How large can the cost of doing full-fledged market research be and still be worthwhile?
=c. Assume now that the estimate of $1 million for the cost of doing full-fledged market research is correct but that there is some uncertainty in the financial data ($15 million, $6 million, and
=9.25. You are given the following decision tree, where the numbers in parentheses are probabilities and the numbers on the right are payoffs at these terminal points.a. Analyze this decision tree to
=9.27.* The Athletic Department of Leland University is considering whether to hold an extensive campaign next year to raise funds for a new athletic field. The response to the campaign depends
=a. Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table.
=b. According to Bayes’ decision rule, should the campaign be undertaken?
=c. What is the expected value of perfect information?
=d. A famous football guru, William Walsh, has offered his services to help evaluate whether the team will have a winning season. For $100,000, he will carefully evaluate the team throughout spring
=Te. Use the corresponding Excel template to obtain the answers requested in part d.
=f. Draw the decision tree for this entire problem by hand. Analyze this decision tree to determine the optimal policy regarding whether to hire William and whether to undertake the campaign.A g. Use
=A h. Find the expected value of sample information. If the fee for hiring William Walsh is open to negotiation, how large can William’s fee be and still be worthwhile?
=9.31.* The Morton Ward Company is considering the introduction of a new product that is believed to have a 50–50 chance of being successful. One option is to try out the product in a test
=a. Discarding the test market option, develop a decision analysis formulation of the problem by identifying the decision alternatives, states of nature, and payoff table. Then apply Bayes’
=b. Find the expected value of perfect information.
=Ac. Now including the option of trying out the product in a test market, use TreePlan (and the Excel template for posterior probabilities) to construct and solve the decision tree for this problem.
=Ad. Find the expected value of sample information. How large can the cost of trying out the product in a test market be and still be worthwhile to do?
=Ae. Assume now that the estimate of $2 million for the cost of trying out the product in a test market is correct. However, there is some uncertainty in the stated profit and loss figures ($40
=f. Because of the uncertainty described in parte, use SensIt to generate a graph that plots the expected profit over the range of variability for each of the two financial figures (without any
=A g. Generate the corresponding spider chart and tornado chart. Interpret each one.
=A9.32. Chelsea Bush is an emerging candidate for her party’s nomination for president of the United States. She now is considering whether to run in the high-stakes Super Tuesday primaries. If
=A9.33. The executive search being conducted for Western Bank by Headhunters Inc. may finally be bearing fruit. The position to be filled is a key one—vice president for Information
=a. Construct and solve the decision tree for this problem to identify the optimal policy.
=b. Now suppose that Headhunters’s fee for administering its detailed investigative process is negotiable. What is the maximum amount that Western Bank should pay?
=9.35. Reconsider the Goferbroke Co. case study, including the application of utilities in Section 9.9. Max Flyer now has decided that, given the company’s precarious financial situation, he needs
=9.36.* You live in an area that has a possibility of incurring a massive earthquake, so you are considering buying earthquake insurance on your home at an annual cost of $180. The probability of an
=a. Apply Bayes’ decision rule to determine which alternative (take the insurance or not) maximizes your expected assets after one year.b. You now have constructed a utility function that
=9.38. Reconsider Problem 9.37. You now are uncertain about what your true utility function for receiving money is, so you are in the process of constructing this utility function by using the
=9.39. You wish to construct your personal utility function U(M) for receiving M thousand dollars. After setting U(0)0, you next set U(10) 1 as your utility for receiving $10,000.You next want to
=9.40. You are given the following payoff table:Outcome Probability Receive $10,000 0.3 Receive $30,000 0.7 State of Nature Alternative S1 S2 A1 25 36 A2 100 0 A3 0 49 Prior probability p 1 p Outcome
=A9.43. Reconsider the Goferbroke Co. case study when using utilities, as presented in Section 9.9.
=a. Beginning with the decision tree shown in Figure 9.28 (available in one of this chapter’s Excel files), prepare to perform sensitivity analysis by expanding and organizing the spreadsheet to
=b. Perform sensitivity analysis by re-solving the decision tree (after using the Excel template for posterior probabilities to revise these probabilities) when the prior probability of oil is
=a. Use TreePlan to construct and solve a decision tree to decide what to do. What is the best course of action, assuming your goal is to maximize your expected winnings?
=b. Use the equivalent lottery method to determine your personal utility function (in particular, your utility values for all of the possible payoffs in the game).
=c. Re-solve the decision tree, replacing the payoffs with your utility values, to maximize your expected utility. Does the best course of action change?
=a. Suppose that the test marketing is done. Use the Posterior Probabilities template to determine the likelihood that the BPAF would sell well if fully marketed, given that it sells well in the test
=b. Use TreePlan to develop and solve a decision tree to help University Toys decide the best course of action and the expected payoff.
=c. Now suppose that University Toys is uncertain of the probability that the LSPAFs will enter the market before the test marketing would be completed (if it were done). How would you expect the
=d. Generate a data table that shows how the expected payoff and the test marketing decision changes as the probability that the LSPAFs will enter the market varies from 0 percent to 100 percent (at
=e. At what probability does the test marketing decision change?
=a. For the initial analysis, ignore the opportunity of obtaining more information by hiring the marketing research company.Identify the decision alternatives and the states of nature.Construct the
=b. What is Charlotte’s decision if she uses the maximum likelihood criterion?
=c. What is Charlotte’s decision if she uses Bayes’ decision rule?
=d. Now consider the possibility of doing the market research.Develop the corresponding decision tree. Calculate the relevant probabilities and analyze the decision tree. Should Cerebrosoft pay the
=a. Organize the available data on cost and profit estimates in a table.
=b. Formulate the problem in a decision tree. Clearly distinguish between decision and event nodes.
=c. Calculate the expected payoffs for each node in the decision tree.
=d. What is BAAG’s optimal policy according to Bayes’ decision rule?
=e. What would be the expected value of perfect information on the outcome of the research effort?
=f. What would be the expected value of perfect information on the outcome of the development effort?
=g. Marc is a risk-averse decision maker. In a number of interviews, his utility function for money was assessed to be U1M2 1 e
=where M is the company’s net profit in units of hundreds of thousands of dollars (e.g., M 8 would imply a net profit of$800,000). Using Marc’s utility function, calculate the utility for each
=h. Determine the expected utilities for all nodes in the decision tree.
=i. Based on Marc’s utility function, what is BAAG’s optimal policy?
=j. Based on Marc’s utility function, what would be the expected value of perfect information on the outcome of the research effort?
=k. Based on Marc’s utility function, what would be the expected value of perfect information on the outcome of the development effort?
=c,d, e,f. Repeat partsd, e,f, g of Case 3-5 under the new school board decision to prohibit splitting of residential areas among multiple schools.
=b. Referring to part c of Case 3-5, determine how much the total busing cost increases because of the decision to prohibit the splitting of residential areas among multiple schools.
=a. Formulate and solve a BIP model for this problem under the current policy of providing busing for all middle school students who must travel more than approximately a mile.
=e. How would the inventory policy be affected if the items composing a kitchen set could not be replenished immediately?Under what conditions is the assumption of immediate replenishment
=d. Brenda convinces management that the kitchen department should serve as a testing ground for future inventory policies.To provide adequate space for testing, management decides to allocate all
=c. Furniture City decides to discontinue carrying nursery sets, and the warehouse space previously allocated to the nursery department is divided between the existing departments at Furniture City.
=b. How many of each feature and style should Furniture City stock in the local warehouse? How many different kitchen sets are in stock?
=a. Formulate and solve a binary integer programming problem to maximize the total number of kitchen sets (and thus the number of customer orders) Furniture City stocks in the local warehouse. Assume
=c. An influential patron of Rita Losky’s work who chairs the museum’s board of directors learns that Celeste requires at least 20 pieces in the exhibit. He offers to pay the minimum amount
=b. To ensure that the exhibit draws the attention of the public, Celeste decides that it must include at least 20 pieces. Formulate and solve a binary integer programming problem to minimize the

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