Dynamic Programming: Exam Study Guide - Chapter 21, Exams of Information Technology

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Chapter 21: Dynamic

Programming

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1. Dynamic programming requires that its subproblems be independent of one another. a. True b. False ANSWER: False POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.21.01 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.1 A Shortest-Route Problem KEYWORDS: Bloom's: Remember
2. Dynamic programming, when used for the shortest-route problem, requires complete enumeration of paths from the beginning to ending node. a. True b. False ANSWER: False POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.21.01 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.1 A Shortest-Route Problem KEYWORDS: Bloom's: Remember
3. The solution of stage k of a dynamic programming problem is dependent upon the solution of stage k−1. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.21.02 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Understand
4. The output of stage k is the input for stage k−1. a. True b. False

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TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Understand

5. State variables are a function of a state variable and a decision. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.21.02 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.2 A Dynamic Programming Notation KEYWORDS: Bloom's: Understand
6. The return function for a shortest-route problem refers to two directional arcs between nodes. a. True b. False ANSWER: False POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.21.01 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.1 A Shortest-Route Problem KEYWORDS: Bloom's: Remember
7. In solving a shortest-route problem using dynamic programming, the stages represent how many arcs you are from the terminal node. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.21.01 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.1 A Shortest-Route Problem KEYWORDS: Bloom's: Understand
8. As opposed to a specific technique such as linear programming, dynamic programming is considered a general approach. a. True

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b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.21.01 - 21.

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optimal solution. a. True b. False ANSWER: False POINTS: 1

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DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.21.03 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.3 The Knapsack Problem KEYWORDS: Bloom's: Understand

13. The subscripts used in dynamic programming notation refer to states. a. True b. False ANSWER: False POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.21.02 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Remember
14. In order to use dynamic programming, one must be able to view the problem as a multistage decision problem. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.21.02 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Understand
15. Finding the optimal solution to each stage of a dynamic programming problem will always lead to an optimal solution to the total problem. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.21.02 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Understand

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DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.21.02 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Understand

17. An input state variable and an output state variable together define the condition of the process at the beginning and end of a stage.

a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.21.02 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Remember

18. A knapsack problem is so named because the objective is to find the number of N items, each of which has a different weight and value, that can be placed in a knapsack with limited weight capacity so as to maximize the total value of the items placed in the knapsack. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.21.03 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.3 The Knapsack Problem KEYWORDS: Bloom's: Remember

Multiple Choice

19. Stages of a dynamic programming solution procedure a. represent parts of a large mathematical model. b. often represent a sequence of decisions made over time. c. are usually not independent of each other. d. All of these are correct. ANSWER: d

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POINTS: 1

DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.21.01 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.1 A Shortest-Route Problem

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TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Remember

23. A return function is a value such as profit or loss associated with making decision dn at a. stage n for a specific value of output variable xn.

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b. stage n for a specific value of input variable xn. c. stage n for a specific value of stage m. d. input n for a specific value of output variable xn. ANSWER: b POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.21.01 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.1 A Shortest-Route Problem KEYWORDS: Bloom's: Understand

24. If x 3 = t 4 (x 4 ,d 4 ) = x 4 − 2d 4 and r 4 (x 4 ,d 4 ) = 16d 4 , the state variable is a. t. b. x. c. r. d. d. ANSWER: b POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.21.02 - 21. NATIONAL STANDARDS: United States - BUSPROG: Analytic TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Apply
25. If x 3 = t 4 (x 4 ,d 4 ) = x 4 − 2d 4 and r 4 (x 4 ,d 4 ) = 16d 4 , the stage transformation function is a. t. b. x. c. r. d. d. ANSWER: a POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.21.02 - 21. NATIONAL STANDARDS: United States - BUSPROG: Analytic TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Apply
26. If x 3 = t 4 (x 4 ,d 4 ) = x 4 − 2d 4 and r 4 (x 4 ,d 4 ) = 16d 4 , the subscripts refer to a. state.

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POINTS: 1

DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.21.02 - 21. NATIONAL STANDARDS: United States - BUSPROG: Analytic TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Apply

27. The knapsack problem is to determine how many units of each item to place in the knapsack to a. minimize total value. b. maximize total value. c. minimize the number of items in the knapsack. d. maximize the number of items in the knapsack. ANSWER: b POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.21.03 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.3 The Knapsack Problem KEYWORDS: Bloom's: Remember
28. Solutions in dynamic programming a. are not optimal. b. are unique. c. represent each stage. d. All of these are correct. ANSWER: c POINTS: 1 DIFFICULTY: Easy LEARNING OBJECTIVES: IMS.ASWC.19.21.02 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Understand

Subjective Short Answer

29. Find the shortest path through the following network using dynamic programming.

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ANSWER:

STAGE 1

Input Node Decision Arc Shortest Distance 8 8−10 4 9 9−10 3 STAGE 2 Input Node Decision Arc Shortest Distance 5 5−9 6 6 6−8 10 7 7−8 11 STAGE 3 Input Node Decision Arc Shortest Distance 2 2−5 16 3 3−5 13 4 4−6 17 STAGE 4 Input Node Decision Arc Shortest Distance 1 1−4 19 POINTS: 1 DIFFICULTY: Challenging LEARNING OBJECTIVES: IMS.ASWC.19.21.01 - 21. NATIONAL STANDARDS: United States - BUSPROG: Analytic TOPICS: 21.1 A Shortest-Route Problem KEYWORDS: Bloom's: Analyze

30. Audio Disks will be opening outlets in the greater Phoenix area. The estimated sales at each store are dependent not only on the store location, but also on the number of sales personnel, as presented in the table below ($1000s/year). Each store requires at least two salespeople, and a pool of nine salespeople is available.

Staff Size 3 4 5 Store 1 60 85 90 100 Store 2 105 120 130 150 Store 3 120 145 160 175

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stage (store).

b.

c. Alternate optimal solutions: Store Salespeople Sales Salespeople Sales 1 2 3

Total sales 350 350

POINTS: 1 DIFFICULTY: Challenging LEARNING OBJECTIVES: IMS.ASWC.19.21.02 - 21. NATIONAL STANDARDS: United States - BUSPROG: Analytic TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Evaluate

31. Consider the following integer linear program:

Max (^) 5x 1 + 7x 2 + 9x 3 s.t. (^) 2x 1 + 3x 2 + 4x 3 ≤ 8 x 1 ≤ 3 x 2 ≤ 2 x 1 , x 2 , x 3 ≥ 0, integer

a. Set up the network that represents the dynamic programming formulation. b. Solve the problem using dynamic programming. ANSWER:

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a.

b. (^) x 1 = 1, x 2 = 2, x 3 = 0 POINTS: 1 DIFFICULTY: Challenging LEARNING OBJECTIVES: IMS.ASWC.19.21.02 - 21. NATIONAL STANDARDS: United States - BUSPROG: Analytic TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Create

32. A driver wants to make a trip from city 1 to city 7. The road mileage between cities is given below. Find the shortest route.

To City From City 1 2 3 4 5 6 7 1 − 2 2 4 − − − 2 − − − − 4 10 − 3 − − − − 12 6 − 4 − − − − 10 − − 5 − − − − − − 14 6 − − − − − − 2 7 − − − − − − −

ANSWER: 1-3-6-7; 13 miles POINTS: 1 DIFFICULTY: Challenging LEARNING OBJECTIVES: IMS.ASWC.19.21.01 - 21. NATIONAL STANDARDS: United States - BUSPROG: Analytic TOPICS: 21.1 A Shortest-Route Problem KEYWORDS: Bloom's: Evaluate