Integer Linear Programming Exam Study Guide: Chapter 7, Exams of Information Technology

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True / False

1. The LP Relaxation contains the objective function and constraints of the IP problem, but drops all integer restrictions. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.07.02 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.2 Graphical and Computer Solutions for an All-Integer Linear Program KEYWORDS: Bloom's: Understand
2. In general, rounding large values of decision variables to the nearest integer value causes fewer problems than rounding small values. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.07.02 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.2 Graphical and Computer Solutions for an All-Integer Linear Program KEYWORDS: Bloom's: Understand
3. If the optimal solution to the LP Relaxation problem is an integer, it is the optimal solution to the integer linear program. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.07.02 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking

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NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.3 Applications Involving 0-1 Variables KEYWORDS: Bloom's: Understand

5. A multiple-choice constraint involves selecting k out of n alternatives, where k ≥ 2. a. True b. False ANSWER: False POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.04 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.4 Modeling Flexibility Provided by 0-1 Integer Variables KEYWORDS: Bloom's: Understand
6. In a model involving fixed costs, the 0-1 variable guarantees that the capacity is not available unless the cost has been incurred. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.03 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.3 Applications Involving 0-1 Variables KEYWORDS: Bloom's: Understand
7. If x 1 + x 2 ≤ 500y 1 and y 1 is 0-1, then if y 1 is 0, x 1 and x 2 will be 0. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.03 - 7.

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NATIONAL STANDARDS: United States - BUSPROG: Analytic TOPICS: 7.3 Applications Involving 0-1 Variables KEYWORDS: Bloom's: Apply

8. The constraint x 1 + x 2 + x 3 + x 4 ≤ 2 means that two out of the first four projects must be selected. a. True b. False ANSWER: False POINTS: 1 DIFFICULTY: Easy

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DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.07.02 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.2 Graphical and Computer Solutions for an All-Integer Linear Program KEYWORDS: Bloom's: Understand

12. The computer output for integer programs in the textbook does not include reduced costs, dual values, or sensitivity ranges because these variables are not meaningful for integer programs.

a. True

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b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.07.02 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.2 Graphical and Computer Solutions for an All-Integer Linear Program KEYWORDS: Bloom's: Understand

13. Some linear programming problems have a special structure that guarantees the variables will have integer values. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.07.01 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.1 Types of Integer Linear Programming Models KEYWORDS: Bloom's: Remember
14. Generally, the optimal solution to an integer linear program is less sensitive to the constraint coefficients than is a linear program. a. True b. False ANSWER: False POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.07.04 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.4 Modeling Flexibility Provided by 0-1 Integer Variables KEYWORDS: Bloom's: Understand
15. For the classic assignment problem, the optimal linear programming solution will consist of 0s and 1s. a. True

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a. True b. False ANSWER: False POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.04 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.4 Modeling Flexibility Provided by 0-1 Integer Variables KEYWORDS: Bloom's: Understand

17. If the LP Relaxation of an integer program has a feasible solution, then the integer program has a feasible solution. a. True b. False ANSWER: False POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.02 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.2 Graphical and Computer Solutions for an All-Integer Linear Program KEYWORDS: Bloom's: Understand
18. Binary variables can be used to model multiple-choice and mutually exclusive constraints. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.07.04 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.4 Modeling Flexibility Provided by 0-1 Integer Variables KEYWORDS: Bloom's: Remember
19. Most practical applications of integer linear programming involve only 0-1 integer variables. a. True

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b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.07.03 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.3 Applications Involving 0-1 Variables KEYWORDS: Bloom's: Remember

20. Integer linear programs provide substantial modeling flexibility and thus are harder to solve than linear programs.

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TOPICS: 7.1 Types of Integer Linear Programming Models KEYWORDS: Bloom's: Understand

23. In a model, x 1 ≥ 0 and integer, x 2 ≥ 0, and x 3 = 0, 1. Which of the following solutions would NOT be feasible? a. x 1 = 5, x 2 = 3, x 3 = 0 b. x 1 = 4, x 2 = 0.389, x 3 = 1 c. x 1 = 2, x 2 = 3, x 3 = 0. d. x 1 = 0, x 2 = 8, x 3 = 0

ANSWER: c

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DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.01 - 7. NATIONAL STANDARDS: United States - BUSPROG: Analytic TOPICS: 7.1 Types of Integer Linear Programming Models KEYWORDS: Bloom's: Analyze

24. Rounded solutions to linear programs must be evaluated for a. feasibility and optimality. b. sensitivity and duality. c. relaxation and boundedness. d. All of these are correct. ANSWER: a POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.02 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.2 Graphical and Computer Solutions for an All-Integer Linear Program KEYWORDS: Bloom's: Understand
25. Rounding the solution of an LP Relaxation to the nearest integer values provides a(n) a. feasible but not necessarily optimal integer solution. b. integer solution that is optimal. c. integer solution that might be neither feasible nor optimal. d. infeasible solution. ANSWER: c POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.02 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.2 Graphical and Computer Solutions for an All-Integer Linear Program KEYWORDS: Bloom's: Understand
26. The solution to the LP Relaxation of a maximization integer linear program provides a(n)

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KEYWORDS: Bloom's: Understand

27. The graph of a problem that requires x 1 and x 2 to be integer has a feasible region a. the same as its LP Relaxation. b. consisting of dots. c. consisting of horizontal stripes. d. consisting of vertical stripes. ANSWER: b POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.02 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.2 Graphical and Computer Solutions for an All-Integer Linear Program KEYWORDS: Bloom's: Understand
28. The 0-1 variables in the fixed cost models correspond to a. a process for which a fixed cost occurs. b. the number of products produced. c. the number of units produced. d. the actual value of the fixed cost. ANSWER: a POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.03 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.3 Applications Involving 0-1 Variables KEYWORDS: Bloom's: Understand
29. Sensitivity analysis for integer linear programming a. can be provided only by computer. b. has precisely the same interpretation as that from linear programming. c. does not have the same interpretation as that from linear programming and should be disregarded. d. is most useful for 0-1 models. ANSWER: c

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DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.04 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.4 Modeling Flexibility Provided by 0-1 Integer Variables KEYWORDS: Bloom's: Understand

30. Let x 1 and x 2 be 0-1 variables whose values indicate whether projects 1 and 2 are/are not done. Which of the

following answers indicates that project 2 can be done only if project 1 is done? a. x 1 + x 2 = 1

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DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.04 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.4 Modeling Flexibility Provided by 0-1 Integer Variables KEYWORDS: Bloom's: Understand

33. In an all-integer linear program, a. all objective function coefficients must be integer. b. all right-hand-side values must be integer. c. all variables must be integer.

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d. all objective function coefficients and right-hand-side values must be integer. ANSWER: c POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.01 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.1 Types of Integer Linear Programming Models KEYWORDS: Bloom's: Understand

34. To perform sensitivity analysis involving an integer linear program, it is best to a. use the dual prices very cautiously. b. make multiple computer runs. c. use the same approach as you would for a linear program. d. use LP Relaxation. ANSWER: b POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.04 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.4 Modeling Flexibility Provided by 0-1 Integer Variables KEYWORDS: Bloom's: Understand
35. Modeling a fixed cost problem as an integer linear program requires a. adding the fixed costs to the corresponding variable costs in the objective function. b. using 0-1 variables. c. using multiple-choice constraints. d. using LP Relaxation. ANSWER: b POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.07.03 - 7. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 7.3 Applications Involving 0-1 Variables KEYWORDS: Bloom's: Understand