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Dynamic Programming Practice Questions, Exams of Mathematics

Walden UniversityMathematics

A series of true/false and multiple-choice questions related to dynamic programming, a method for solving complex problems by breaking them down into simpler subproblems. The questions cover fundamental concepts such as shortest-route problems, dynamic programming notation, knapsack problems, and production and inventory control problems. Each question includes an answer, points, difficulty level, learning objectives, national standards, topics, and keywords to aid in understanding and review. This resource is designed to test and reinforce knowledge of dynamic programming principles and their applications in various optimization scenarios. It is useful for students and professionals seeking to enhance their understanding of dynamic programming techniques and their practical implications. A structured approach to learning and assessing comprehension of dynamic programming concepts, making it a valuable tool for exam preparation and self-study.

Typology: Exams

2024/2025

Available from 08/28/2025

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CH 21 - Dynamic Programming
Page 1
True / False
1. Dynamic programming requires that its subproblems be
independent of one another.
a.
True
b.
False
ANSWER:
POINTS:
DIFFICULTY:
LEARNING OBJECTIVES:
NATIONAL STANDARDS:
TOPICS:
KEYWORDS:
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:
POINTS:
DIFFICULTY:
LEARNING OBJECTIVES:
NATIONAL STANDARDS:
TOPICS:
KEYWORDS:
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pf4
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pfa
pfd
pfe
pff
pf12
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Download Dynamic Programming Practice Questions and more Exams Mathematics in PDF only on Docsity!

True / False

  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
  1. 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
  2. The output of stage k is the input for 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
  3. State variables are a function of a state variable and a decision. a. True b. False ANSWER: True

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

  1. As opposed to a specific technique such as linear programming, dynamic programming is considered a general approach. 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: Remember
  2. Dynamic programming must only involve a finite number of decision alternatives and a finite number of stages. 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: Understand

  1. Dynamic programming is a general approach used when it is possible to break a large problem into interrelated smaller problems, with stage decisions proceeding recursively, solving one of the smaller problems at each stage. 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
  2. In a production and inventory control problem, the states can correspond to the amount of inventory on hand at the beginning of each period. a. True b. False ANSWER: True POINTS: 1 DIFFICULTY: Moderate LEARNING OBJECTIVES: IMS.ASWC.19.21.04 - 21. NATIONAL STANDARDS: United States - BUSPROG: Reflective Thinking

KEYWORDS: Bloom's: Remember

  1. 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
  2. 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
  1. The stage transformation function identifies which state one reaches at the next stage for a given decision. 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
  2. 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
  3. A knapsack problem is so named because the objective is to

KEYWORDS: Bloom's: Understand

  1. The stage transformation function a. transforms the input into the output. b. transforms a stage into a state. c. is a different function for each stage. d. None of these are correct. ANSWER: a 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
  2. State variables in a shortest-route problem represent a. decisions. b. locations in the network. c. the minimum distance between nodes. d. None of these are correct. ANSWER: b 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
  1. The function that “transforms” the input of the stage into the output of the stage is referred to as a stage transformation function and a. is always linear. b. calculates the return of the transformation. c. determines the output of the stage. d. All of these are correct. ANSWER: c 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
  2. 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. 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

KEYWORDS: Bloom's: Apply

  1. 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. b. stage. c. transformation. d. return. 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
  2. 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

  1. 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
  2. Find the shortest path through the following network using dynamic programming. ANSWER: STAGE 1

least two salespeople, and a pool of nine salespeople is available. Staff Size 2 3 4 5 Store 1

Store 2

Store 3

a. What would the states be in the dynamic programming formulation? b. Draw the network that represents the dynamic programming formulation. c. Given the above network, solve the sales personnel allocation problem by finding the longest path. ANSWER: a. The states represent the number of salespeople available at each stage (store). b.

c. Alternate optimal solutions: Stor e Salespeo ple Sales Salespeo ple Sales 1 3 85 3 85 2 3 120 2 105 3 3 145 4 160 Tot al sale s

POINTS: 1

DIFFICULTY: Challenging LEARNING OBJECTIV ES:

IMS.ASWC.19.21.02 - 21.

NATIONAL STANDAR

DS:

United States - BUSPROG: Analytic TOPICS: 21.2 Dynamic Programming Notation KEYWORDS: Bloom's: Evaluate

  1. 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.

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

  1. The owner of a small construction firm is excavating at three sites. He wishes to assign his five additional trucks in such a way as to minimize his total costs. Each site can use zero to three additional trucks; no site can use more than three trucks efficiently. The following site total costs are known. Number Cost of Excavating of Trucks Site 1 Site 2 Site 3 0 $10,000 $15,000 $20, 1 10,000 14,000 18, 2 9,200 13,250 17, 3 8,500 12,750 17, a. Use dynamic programming to find the assignment of the additional trucks that minimizes total cost. b. If the owner had only four trucks to assign, what would be the optimal assignment and total cost?

ANSWER:

a. The minimal cost truck assignments are: 0 trucks to site 1 3 trucks to site 2 2 trucks to site 3 at a cost of $40,250. b. There are two optimal assignments: Site 1 0 trucks 0 trucks Site 2 3 trucks or 2 trucks Site 3 1 truck 2 trucks at a cost of $40,750. 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

  1. A number of types of items are to be shipped as cargo. The total available weight in the truck is 10 tons. Determine the number of units of items to be shipped to maximize profit. Item Weight (tons) Profit ($1000s) A 3 5 B 4 7 C 2 3