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Chapter 3 - Linear Programming:

Sensitivity Analysis and

Interpretation of Solution

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Analysis and Interpretation of Solution

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True / False

1. Classical sensitivity analysis provides no information about changes resulting from a change in the coefficient of a variable in a constraint. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.03.04 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.4 Limitations of Classical Sensitivity Analysis KEYWORDS: Bloom's: Understand
2. The reduced cost of a variable is the dual value of the corresponding nonnegativity constraint. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.03.03 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.3 Sensitivity Analysis: Computer Solution KEYWORDS: Bloom's: Understand
3. When the right-hand sides of two constraints are each increased by one unit, the objective function value will be adjusted by the sum of the constraints' dual prices. a. True b. False ANSWER: False POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.03.02 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.2 Graphical Sensitivity Analysis KEYWORDS: Bloom's: Understand

Analysis and Interpretation of Solution

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LEARNING OBJECTIVES: IMS.ASWC.19.03.03 - 3.

NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.3 Sensitivity Analysis: Computer Solution KEYWORDS: Bloom's: Apply

5. When two or more objective function coefficients are changed simultaneously, further analysis is necessary to determine whether the optimal solution will change. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.03.02 - 3. NATIONAL STANDARDS: United States - BUSPROG: Analytic TOPICS: 3.2 Graphical Sensitivity Analysis KEYWORDS: Bloom's: Understand
6. The dual value and dual price are identical for a minimization problem. a. True b. False ANSWER: False POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.A3.02 - A3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: Appendix 3.2 Sensitivity Analysis with Lingo KEYWORDS: Bloom's: Understand
7. A negative dual price indicates that increasing the right-hand side of the associated constraint would be detrimental to the objective. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.03.02 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking

Analysis and Interpretation of Solution

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TOPICS: 3.2 Graphical Sensitivity Analysis KEYWORDS: Bloom's: Understand

8. In order to tell the impact of a change in a constraint coefficient, the change must be made and then the model resolved. a. True b. False ANSWER: True POINTS: 1

Analysis and Interpretation of Solution

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TOPICS: 3.2 Graphical Sensitivity Analysis KEYWORDS: Bloom's: Understand

12. There is a dual price for every decision variable in a model. a. True b. False ANSWER: False

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POINTS: 1

DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.03.03 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.3 Sensitivity Analysis: Computer Solution 3.2 Graphical Sensitivity Analysis KEYWORDS: Bloom's: Understand

13. The amount of a sunk cost will vary depending on the values of the decision variables. a. True b. False ANSWER: False POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.03.03 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.3 Sensitivity Analysis: Computer Solution KEYWORDS: Bloom's: Understand
14. If the optimal value of a decision variable is zero and its reduced cost is zero, this indicates that alternative optimal solutions exist. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.A3.01 - A3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: Appendix 3.1 Sensitivity Analysis with Excel Solver KEYWORDS: Bloom's: Understand
15. Relevant costs should be reflected in the objective function, but sunk costs should not. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy

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b. False ANSWER: False POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.03.03 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.3 Sensitivity Analysis: Computer Solution KEYWORDS: Bloom's: Apply

17. If the dual price for the right-hand side of a ≤ constraint is zero, there is no upper limit on its range of feasibility. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.03.02 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.2 Graphical Sensitivity Analysis KEYWORDS: Bloom's: Understand
18. Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution. a. True b. False ANSWER: False POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.03.02 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.2 Graphical Sensitivity Analysis KEYWORDS: Bloom's: Understand
19. If two or more objective function coefficients are changed simultaneously, further analysis is necessary to determine whether the optimal solution will change. a. True b. False ANSWER: True POINTS: 1

Analysis and Interpretation of Solution

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DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.03.02 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.2 Graphical Sensitivity Analysis KEYWORDS: Bloom's: Understand

Multiple Choice

Analysis and Interpretation of Solution

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TOPICS: 3.3 Sensitivity Analysis: Computer Solution KEYWORDS: Bloom's: Understand

23. A constraint with a positive slack value a. will have a positive dual price. b. will have a negative dual price. c. will have a dual price of zero.

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d. has no restrictions for its dual price. ANSWER: c POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.03.03 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.3 Sensitivity Analysis: Computer Solution KEYWORDS: Bloom's: Understand

24. The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the a. optimal solution. b. dual solution. c. range of optimality. d. range of feasibility. ANSWER: c POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.03.02 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.2 Graphical Sensitivity Analysis KEYWORDS: Bloom's: Remember
25. The range of feasibility measures a. the right-hand-side values for which the objective function value will not change. b. the right-hand-side values for which the values of the decision variables will not change. c. the right-hand-side values for which the dual prices will not change. d. All of these are correct. ANSWER: c POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.03.03 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.3 Sensitivity Analysis: Computer Solution KEYWORDS: Bloom's: Remember
26. An objective function reflects the relevant cost of labor hours used in production rather than treating them as a sunk

Analysis and Interpretation of Solution

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DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.03.03 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.3 Sensitivity Analysis: Computer Solution KEYWORDS: Bloom's: Understand

27. The graphical solution procedure is useful only for linear programs involving a. two decision variables. b. more than two decision variables. c. a single constraint. d. None of these are correct. ANSWER: a POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.03.03 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.3 Sensitivity Analysis: Computer Solution KEYWORDS: Bloom's: Understand
28. An improvement in the value of the objective function per unit increase in a right-hand side is the a. sensitivity value. b. constraint coefficient. c. slack value. d. None of these are correct. ANSWER: d POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.03.02 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.2 Graphical Sensitivity Analysis KEYWORDS: Bloom's: Understand
29. The amount the objective function coefficient of a decision variable would have to improve before that variable would have a positive value in the solution is the a. dual price. b. surplus variable. c. reduced cost.

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d. upper limit. ANSWER: c POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.03.03 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.3 Sensitivity Analysis: Computer Solution

Analysis and Interpretation of Solution

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NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.3 Sensitivity Analysis: Computer Solution KEYWORDS: Bloom's: Understand

33. Which of the following is NOT a question answered by standard sensitivity analysis information? a. If the right-hand-side value of a constraint changes, will the objective function value change? b. Over what range can a constraint's right-hand-side value change without the constraint's dual price possibly

Analysis and Interpretation of Solution

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changing? c. By how much will the objective function value change if the right-hand-side value of a constraint changes beyond the range of feasibility? d. By how much will the objective function value change if a decision variable's coefficient in the objective function changes within the range of optimality? ANSWER: c POINTS: 1 DIFFICULTY: Challenging LEARNING OBJECTIVES: IMS.ASWC.19.03.03 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.3 Sensitivity Analysis: Computer Solution KEYWORDS: Bloom's: Understand

34. The cost that varies depending on the values of the decision variables is a a. reduced cost. b. relevant cost. c. sunk cost. d. dual cost. ANSWER: b POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.03.03 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.3 Sensitivity Analysis: Computer Solution KEYWORDS: Bloom's: Remember
35. A cost that is incurred no matter what values the decision variables assume is a(n) a. reduced cost. b. optimal cost. c. sunk cost. d. dual cost. ANSWER: c POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.03.03 - 3. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 3.3 Sensitivity Analysis: Computer Solution