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ch5s Student: _ 1. Decision trees, with their predetermined analysis of a situation, are really not useful in making health care decisions since every person is unique. True False 2. Bounded rationality refers to the limits imposed on decisionmaking because of costs, human abilities, time, technology, and/or availability of information. True False 3. In reaching a decision, the alternative with the lowest cost should be ranked #1. True False 4. The expected monetary value approach is most appropriate when the decisionmaker is riskneutral. True False 5. The value of perfect information is inversely related to losses predicted. True False 6. Expected monetary value gives the longrun average payoff if a large number of identical decisions could be made. True False 7. Among decision environments, risk implies that certain parameters have probabilistic outcomes. True False 8. Among decision environments, uncertainty implies that states of nature have wide ranging probabilities associated with them. True False 9. In decision theory, states of nature refer to possible future conditions. True False 10. The maximin approach involves choosing the alternative with the highest payoff. True False 11. The maximin approach involves choosing the alternative that has the "best worst" payoff. True False 12. The Laplace criterion treats states of nature as being equally likely. True False 13. The maximax approach is a pessimistic strategy. True False 14. A weakness of the maximin approach is that it loses some information. True False 15. The expected value approach applies to decisionmaking under uncertainty. True False 16. The expected value approach is used for decisionmaking under risk. True False 17. The EVPI indicates an upper limit on the amount a decisionmaker should be willing to spend to obtain additional information. True False 18. Graphical sensitivity analysis is limited to cases with no more than two alternatives. True False 19. Graphical sensitivity analysis is used for decisionmaking under risk. True False 20. An advantage of decision trees compared to payoff tables is that they permit us to analyze situations involving sequential decisions. True False 21. The term suboptimization is best described as the: A. result of individual departments making the best decisions for their own areas B. limitations on decisionmaking caused by costs and time C. result of failure to adhere to the steps in the decision process D. result of ignoring symptoms of the problem E. none of the above 22. Which phrase best describes the term bounded rationality? A. thinking a problem through clearly before acting B. taking care not to exhaust limited resources C. the result of departmentalized decision making D. limits imposed on decision making by costs, time, and technology E. the use of extremely structured steps in the decision making process 23. Testing how a problem solution reacts to changes in one or more of the model parameters is called: A. simulation B. sensitivity analysis C. priority recognition D. analysis of variance E. decision analysis 24. Sensitivity analysis is required because _. A. payoffs and probabilities are estimates B. most decision will affect employees C. expected payoffs are sensitive to the time value of money D. it's the second step in the decision model E. with the passage of time, small decisions get bigger 25. A tabular presentation that shows the outcome for each decision alternative under the various possible states of nature is called a/an: A. payoff table B. feasible region C. LaPlace table D. decision tree E. payback period matrix 26. Which of the following characterizes decisionmaking under uncertainty? A. Decisionmakers must rely on probabilities in assessing outcomes B. The likelihood of possible future events is unknown C. Relevant parameters have known values D. Certain parameters have probabilistic outcomes E. none of the above 27. Which of the following is not an approach for decisionmaking under uncertainty? A. decision trees B. maximin C. maximax D. minimax regret E. Laplace 28. Determining the worst payoff for each alternative and choosing the alternative with the "best worst" is the approach called: A. minimin B. maximin C. maximax D. minimax regret E. Laplace 29. Determining the average payoff for each alternative and choosing the alternative with the highest average is the approach called: A. minimin B. maximin C. maximax D. minimax regret E. Laplace 30. The maximin approach to decisionmaking refers to: A. minimizing the maximum return B. maximizing the minimum return C. maximizing the minimum expected value D. choosing the alternative with the highest payoff E. choosing the alternative with the minimum payoff 31. Which one of these is not used in decisionmaking under risk? A. EVPI B. EMV C. decision trees D. minimax regret E. All are used for risk situations 32. The term opportunity loss or regret is most closely associated with: A. minimax regret B. maximax C. maximin D. expected monetary value E. Laplace 33. The expected monetary value criterion (EMV) is the decisionmaking approach used with the decision environment of: A. certainty B. risk C. uncertainty D. all of the above E. none of the above 34. A decision tree is: A. an algebraic representation of alternatives B. a behavioral representation of alternatives C. a matrix representation of alternatives D. a schematic representation of alternatives E. limited to a maximum of 12 branches 35. The difference between expected payoff under certainty and expected payoff under risk is the expected: A. monetary value B. value of perfect information C. net present value D. rate of return E. profit 36. If the minimum expected regret is computed, it indicates to a decisionmaker the expected: A. value of perfect information B. payoff under certainty C. monetary value D. payoff under risk E. none of the above 37. The term sensitivity analysis is most closely associated with: A. maximax B. maximin C. decisionmaking under risk D. minimax regret E. Laplace criterion 38. A manager has developed the following payoff table that indicates the profits associated with a set of alternatives under two possible states of nature Answer the following questions: (A) If the manager uses maximin as the decision criterion, which of the alternatives would be indicated? (B) If the manager uses minimax regret as the criterion, which alternative would be indicated? (C) Determine the expected value of perfect information if P(S2) = .40 (D) Determine the range of P(S2) for which each alternative would be optimal. 39. A manager's staff has compiled the information below which pertains to four capacity alternatives under four states of nature. Values in the matrix are present value in thousands of dollars (A) Assuming a maximax strategy, which alternative would be chosen? (B) If maximin were used, which alternative would be chosen? (C) If states of nature are equally likely and an expected value criterion of maximization is used, which alternative would be chosen? 40. A manager has learned that annual profits from four alternatives being considered for solving a capacity problem are projected to be $15,000 for A, $30,000 for B, $45,000 for C, and $60,000 for D if state of nature 1 occurs; and $60,000 for A, $80,000 for B, $90,000 for C, and $35,000 for D if state of nature 2 occurs (A) Assuming maximax is used, what alternative would be chosen? (B) Assuming maximin is used, what alternative would be chosen? (C) If P(State of Nature 1) is .40, what alternative has the highest expected monetary value? (D) Determine the range of P(S2) for which each alternative would be optimal. 41. A manager is quite concerned about the recent deterioration of a section of the roof on a building that houses her firm's computer operations. According to her assistant there are three options which merit consideration: A, B, and C. Moreover, there are three possible future conditions that must be included in the analysis: I, which has a probability of occurrence of .5; II, which has a probability of .3; and III, which has a probability of .2 If condition I materializes, A will cost $12,000, B will cost $20,000, and C will cost $16,000. If condition II materializes, the costs will be $15,000 for A, $18,000 for B, and $14,000 for C. If condition III materializes, the costs will be $10,000 for A, $15,000 for B, and $19,000 for C (A) Draw a decision tree for this problem (B) Using expected monetary value, which alternative should be chosen? *PV for profits ($000) 42. The maximax strategy would be: A. buy B. lease C. rent D. high E. low 43. The maximin strategy would be: A. buy B. lease C. rent D. high E. low 44. The minimax regret strategy would be: A. buy B. lease C. rent D. high E. low 45. If P(high) is .60, the choice for maximum expected value would be: A. buy B. lease C. rent D. high E. low *PV for profits ($000) 46. The maximax strategy would be: A. small B. Medium C. med.large D. large E. exlarge 47. The maximin strategy would be: A. small B. Medium C. med.large D. large E. exlarge 48. The minimax regret strategy would be: A. small B. Medium C. med.large D. large E. exlarge 49. If yes and no are equally likely, which alternative has the largest expected monetary value? A. small B. Medium C. med.large D. large E. exlarge *PV for profits ($000) 50. The maximax strategy would be: A. A B. B C. C D. D E. E 96. For what range of probability that the new cable network will be successful will she select the print media strategy? A. 0 .4 B. 0 .55 C. .4 .7 D. .55 1 E. .7 1 When this state of nature is relatively unlikely, this is the best strategy AACSB: Analytic Blooms: Apply Difficulty: Hard Learning Objective: 05s06 Conduct sensitivity analysis on a simple decision problem Stevenson Chapter 05S #96 Topic Area: Sensitivity Analysis 97. For what range of probability that the new cable network will be successful will she select the mixed media strategy? A. 0 .4 B. 0 .55 C. .4 .7 D. .55 1 E. .7 1 This strategy is best when the states of nature are close to one another in likelihood AACSB: Analytic Blooms: Apply Difficulty: Hard Learning Objective: 05s06 Conduct sensitivity analysis on a simple decision problem Stevenson Chapter 05S #97 Topic Area: Sensitivity Analysis 98. For what range of probability that the new cable network will be successful will she select the television media strategy? A. 0 .4 B. 0 .55 C. .4 .7 D. .55 1 E. .7 1 When this state of nature is relatively likely, this is the best option AACSB: Analytic Blooms: Apply Difficulty: Hard Learning Objective: 05s06 Conduct sensitivity analysis on a simple decision problem Stevenson Chapter 05S #98 Topic Area: Sensitivity Analysis The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production. (Due to budgeting constraints, only one new picture can be undertaken at this time.) She feels that script #1 has a 70 percent chance of earning about $10,000,000 over the long run, but a 30 percent chance of losing $2,000,000. If this movie is successful, then a sequel could also be produced, with an 80 percent chance of earning $5,000,000, but a 20 percent chance of losing $1,000,000. On the other hand, she feels that script #2 has a 60 percent chance of earning $12,000,000, but a 40 percent chance of losing $3,000,000. If successful, its sequel would have a 50 percent chance of earning $8,000,000, but a 50 percent chance of losing $4,000,000. Of course, in either case, if the original movie were a "flop," then no sequel would be produced Stevenson Chapter 05S 99. What would be the total payoff if script #1 were a success, but its sequel were not? A. $15,000,000 B. $10,000,000 C. $9,000,000 D. $5,000,000 E. $1,000,000 This is the EMV of the best path that emerges if the first script is a success AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #99 Topic Area: Decision Trees 100. What is the probability that script #1 will be a success, but its sequel will not? A. .8 B. .7 C. .56 D. .2 E. .14 Multiply the two probabilities AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #100 Topic Area: Decision Trees 101. What is the expected value of selecting script #1? A. $15,000,000 B. $9,060,000 C. $8,400,000 D. $7,200,000 E. $6,000,000 This represents the expected value of the payoffs associated with the script #1 branch of the decision tree AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #101 Topic Area: Decision Trees 102. What is the expected value of selecting script #2? A. $15,000,000 B. $9,060,000 C. $8,400,000 D. $7,200,000 E. $6,000,000 This represents the expected value of the payoffs associated with the script #2 branch of the decision tree AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #102 Topic Area: Decision Trees 103. What is the expected value for the optimum decision alternative? A. $15,000,000 B. $9,060,000 C. $8,400,000 D. $7,200,000 E. $6,000,000 Script #1 should be chosen, as its expected value is higher AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #103 Topic Area: Decision Trees One local hospital has just enough space and funds presently available to start either a cancer or heart research lab. If administration decides on the cancer lab, there is a 20 percent chance of getting $100,000 in outside funding from the American Cancer Society next year, and an 80 percent chance of getting nothing. If the cancer research lab is funded the first year, no additional outside funding will be available the second year. However, if it is not funded the first year, then management estimates the chances are 50 percent it will get $100,000 the following year, and 50 percent that it will get nothing again. If, however, Merciless's management decides to go with the heart lab, then there's a 50 percent chance of getting $50,000 in outside funding from the American Heart Association the first year and a 50 percent change of getting nothing. If the heart lab is funded the first year, management estimates a 40 percent chance of getting another $50,000 and a 60 percent chance of getting nothing additional the second year. If it is not funded the first year, then management estimates a 60 percent chance for getting $50,000 and a 40 percent chance for getting nothing in the following year. For both the cancer and heart research labs, no further possible funding is anticipated beyond the first two years Stevenson Chapter 05S 104. What would be the total payoff if the heart lab were funded in both the first and second years? A. $100,000 B. $60,000 C. $50,000 D. $40,000 E. $20,000 The total payoff would be the $50,000 in the first year and the $50,000 in the second year AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #104 Topic Area: Decision Trees 105. What is the probability that the heart lab will be funded in both the first and second years? A. .4 B. .3 C. .2 D. .1 E. 0 Multiple the probability of being funded in the first year by the probability of being funded in the second year AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #105 Topic Area: Decision Trees 106. What is the expected value for the decision alternative to select the cancer lab? A. $100,000 B. $60,000 C. $50,000 D. $40,000 E. $20,000 Weight each payoff by its likelihood of occurrence AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #106 Topic Area: Decision Trees 107. What is the expected value for the decision alternative to select the heart lab? A. $100,000 B. $60,000 C. $50,000 D. $40,000 E. $20,000 Weight each payoff by its likelihood of occurrence AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #107 Topic Area: Decision Trees 108. What is the expected value for the optimum decision alternative? A. $100,000 B. $60,000 C. $50,000 D. $40,000 E. $20,000 Choose the option with the highest expected value AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #108 Topic Area: Decision Trees Two professors at a nearby university want to coauthor a new textbook in either economics or statistics. They feel that if they write an economics book, they have a 50 percent chance of placing it with a major publisher, and it should ultimately sell about 40,000 copies. If they can't get a major publisher to take it, then they feel they have an 80 percent chance of placing it with a smaller publisher, with ultimate sales of 30,000 copies. On the other hand, if they write a statistics book, they feel they have a 40 percent chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If they can't get a major publisher to take it, they feel they have a 50 percent chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies Stevenson Chapter 05S 109. What is the probability that the economics book would wind up being placed with a smaller publisher? A. .8 B. .5 C. .4 D. .2 E. .1 Multiply the probability of it not being placed with a big publisher (.5) times the probability of it then being placed with small publisher (.8) AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #109 Topic Area: Decision Trees 110. What is the probability that the statistics book would wind up being placed with a smaller publisher? A. .6 B. .5 C. .4 D. .3 E. 0 Multiply the probability of it not being placed with a big publisher (.6) times the probability of it then being placed with small publisher (.5) AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #110 Topic Area: Decision Trees 111. What is the expected value for the decision alternative to write the economics book? A. 50,000 copies B. 40,000 copies C. 32,000 copies D. 30,500 copies E. 10,500 copies Multiply the expected value of the small publisher node (24,000 copies) by the likelihood of a large publisher rejecting the book. Multiply the payoff of a large publisher (40,000 copies) by the likelihood of a large publisher accepting the book. Add these together AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #111 Topic Area: Decision Trees 112. What is the expected value for the decision alternative to write the statistics book? A. 50,000 copies B. 40,000 copies C. 32,000 copies D. 30,500 copies E. 10,500 copies Multiply the expected value of the small publisher node (17,500 copies) by the likelihood of a large publisher rejecting the book (.6). Multiply the payoff of a large publisher (50,000 copies) by the likelihood of a large publisher accepting the book. Add these together AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #112 Topic Area: Decision Trees 113. What is the expected value for the optimum decision alternative? A. 50,000 copies B. 40,000 copies C. 32,000 copies D. 30,500 copies E. 10,500 copies The economics textbook has the highest expected value AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem Stevenson Chapter 05S #113 Topic Area: Decision Trees 114. When a decisionmaking scenario involves two or more departments, if the individual departments pursue what is optimal for them, sometimes the overall organization suffers. This is an example of _. A. subminimimization B. suboptimization C. rational boundaries D. decision making under risk E. decision making under uncertainty Suboptimization penalizes the overall organization even though individual departments might be perceived to be better off AACSB: Reflective Thinking Blooms: Remember Difficulty: Easy Learning Objective: 05s01 Describe the different environments under which operations decisions are made Stevenson Chapter 05S #114 Topic Area: Causes of Poor Decisions 115. Which of the following is not a stage in the decision making process? A. select the best alternative B. develop suitable alternatives C. analyze and compare alternatives D. monitor the competition E. specify objectives Monitoring the competition isn't considered part of the decision making process AACSB: Reflective Thinking Blooms: Remember Difficulty: Easy Learning Objective: 05s01 Describe the different environments under which operations decisions are made Stevenson Chapter 05S #115 Topic Area: Causes of Poor Decisions 116. Option A has a payoff of $10,000 in environment 1 and $20,000 in environment 2. Option B has a payoff of $5,000 in environment 1 and $27,500 in environment 2. Once the probability of environment 1 exceeds , option A becomes the better choice. A. .40 B. .45 C. .50 D. .57 E. .60 A is better when the likelihood of environment 1 becomes relatively more likely AACSB: Analytic Blooms: Apply Difficulty: Hard Learning Objective: 05s06 Conduct sensitivity analysis on a simple decision problem Stevenson Chapter 05S #116 Topic Area: Sensitivity Analysis 117. Option A has a payoff of $10,000 in environment 1 and $20,000 in environment 2. Option B has a payoff of $12,500 in environment 1 and $17,500 in environment 2. Once the probability of environment 2 exceeds , option A becomes the better choice. A. .33 B. .67 C. .45 D. .50 E. .55 A is better when environment 2 is relatively more likely AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s06 Conduct sensitivity analysis on a simple decision problem Stevenson Chapter 05S #117 Topic Area: Sensitivity Analysis 118. Which of the following would make decision trees an especially attractive decision making tool? A. The need to think through a possible sequence of decisions B. The need to maximize the expected value of perfect information C. The need to minimize expected regret D. The need to avoid suboptimization E. The need to minimize costs Decision trees are useful when followup decisions might need to be made AACSB: Reflective Thinking Blooms: Remember Difficulty: Easy Learning Objective: 05s01 Describe the different environments under which operations decisions are made Stevenson Chapter 05S #118 Topic Area: Decision Trees Stevenson Chapter 05S 119. If somehow you find out for certain that state of nature #4 is going to occur, which alternative will you select? A=6 Feedback: A would be best in state of nature #4 AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s01 Describe the different environments under which operations decisions are made Stevenson Chapter 05S #119 Topic Area: Decision Making under Certainty 120. If you are uncertain which state of nature will occur, and use the maximin criterion, which alternative will you select? C=2 Feedback: Among worstcase scenarios, C's is best AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s02 Describe and use techniques that apply to decision making under uncertainty Stevenson Chapter 05S #120 Topic Area: Decision Making under Uncertainty 121. If you are uncertain which state of nature will occur, and use the maximax criterion, which alternative will you select? A=6 Feedback: Among bestcase scenarios, A's is best AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s02 Describe and use techniques that apply to decision making under uncertainty Stevenson Chapter 05S #121 Topic Area: Decision Making under Uncertainty 122. If you are uncertain which state of nature will occur, and use the Laplace criterion, which alternative will you select? B=3 Feedback: If you assume the states of nature are equally likely, B's EMV is most attractive AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s02 Describe and use techniques that apply to decision making under uncertainty Stevenson Chapter 05S #122 Topic Area: Decision Making under Uncertainty 123. If you are uncertain which state of nature will occur, and use the minimax regret criterion, which alternative will you select? C=3 Feedback: C will minimize the maximum amount of regret you could experience AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s02 Describe and use techniques that apply to decision making under uncertainty Stevenson Chapter 05S #123 Topic Area: Decision Making under Uncertainty 124. If you feel that P(#1) = .4, P(#2) = .3, P(#3) = .2, and P(#4) = .1, which alternative will you select? B Feedback: Given these likelihoods, B's EMV is most attractive AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s03 Describe and use the expectedvalue approach Stevenson Chapter 05S #124 Topic Area: Decision Making under Risk 125. If you feel that P(#1) = .4, P(#2) = .3, P(#3) = .2, and P(#4) = .1, what is your expected payoff under certainty? EPC=4.1 Feedback: The difference between the expected payoff with perfect information and the expected payoff under risk AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s05 Compute the expected value of perfect information Stevenson Chapter 05S #125 Topic Area: Expected Value of Perfect Information 126. If you feel that P(#1) = .4, P(#2) = .3, P(#3) = .2, and P(#4) = .1, what is your expected value of perfect information? EVPI=1.2 Feedback: This is the difference between what you would get with perfect information and what you will get without it AACSB: Analytic Blooms: Apply Difficulty: Medium Learning Objective: 05s05 Compute the expected value of perfect information Stevenson Chapter 05S #126 Topic Area: Expected Value of Perfect Information ch5s Summary Category # of Questions AACSB: Analytic 86 AACSB: Reflective Thinking 40 Blooms: Apply 86 Blooms: Remember 31 Blooms: Understand Difficulty: Easy Difficulty: Hard 17 Difficulty: Medium 102 Learning Objective: 05s01 Describe the different environments under which operations decisions are made 13 Learning Objective: 05s02 Describe and use techniques that apply to decision making under uncertainty 50 Learning Objective: 05s03 Describe and use the expectedvalue approach 23 Learning Objective: 05s04 Construct a decision tree and use it to analyze a problem 18 Learning Objective: 05s05 Compute the expected value of perfect information 13 Learning Objective: 05s06 Conduct sensitivity analysis on a simple decision problem 15 Stevenson Chapter 05S 140 Topic Area: Causes of Poor Decisions Topic Area: Decision Environments Topic Area: Decision Making under Certainty Topic Area: Decision Making under Risk 22 Topic Area: Decision Making under Uncertainty 51 Topic Area: Decision Trees 20 Topic Area: Expected Value of Perfect Information 15 Topic Area: Introduction Topic Area: Sensitivity Analysis 15 ... it is not funded the first year, then management estimates the chances are 50 percent it will get $100,000 the following year, and 50 percent that it will get nothing again. If, however, Merciless's management decides to go ... year, management estimates a 40 percent chance of getting another $50,000 and a 60 percent chance of getting nothing additional the second year. If it is not funded the first year, then management estimates a 60 percent ... Difficulty: Easy Learning Objective: 05s01 Describe the different environments under which operations decisions are made Stevenson Chapter 05S #1 Topic Area: Decision Trees 2. Bounded rationality refers to the limits imposed on decisionmaking because of costs, human abilities, time,