Question 1

Dynamic programming is a general approach rather than a specific technique.

Accepted Answer

A) True 
 B)False  True

Question 2

Consider the following integer linear program
Max
5x1 + 7x2 + 9x3
s.t.
2x1 + 3x2 + 4x3 ≤ 8
x1 ≤ 3
x2 ≤ 2
x1, x2, x3 ≥ 0, integer
​
a.Set up the network that represents the dynamic programming formulation.
b.Solve the problem using dynamic programming.

Accepted Answer

a. B.x₁ = 1, x₂ = 2, x₃ = 0

Question 3

The output of stage k is the input for stage k−1.

Accepted Answer

A) True 
 B)False  True

Question 4

State variables in a shortest route problem represent

Accepted Answer

A)  decisions. 
B)  locations in the network. 
C)  the minimum distance between nodes. 
D)  None of the alternatives is true. 
A)  decisions. 
B)  locations in the network. 
C)  the minimum distance between nodes. 
D)  None of the alternatives is true.

Question 5

​The stage transformation function identifies which state one reaches at the next stage for a given decision.

Accepted Answer

A) True 
 B)False

Question 6

Dynamic programming must only involve a finite number of decision alternatives and a finite number of stages.

Accepted Answer

A) True 
 B)False

Question 7

A return function is a value such as profit or loss associated with making decision dn at:

Accepted Answer

A)  stage n for 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. 
A)  stage n for 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.

Question 8

Dynamic programming requires that its subproblems be independent of one another.

Accepted Answer

A) True 
 B)False

Question 9

In solving a shortest route problem using dynamic programming the stages represent how many arcs you are from the terminal node.

Accepted Answer

A) True 
 B)False

Question 10

​Ajax Sound is in the business of fabricating printer connection cables. They purchase 30 foot spools of wire from National Electric at $3.00 per spool and cut the wire into various lengths.
​
​Each length of wire is fitted with printer connector jacks at both ends and then packaged. The printer connector jacks cost $.40 per pair (one pair is used in each cable package). Packaging and labor together cost $.20 per package.
​
Because of Ajax's superior marketing skills they are in the enviable position of being able to sell all the printer connection cables they produce. They are currently contemplating offering four different sized cable packages:
​   If unused wire from a spool can be sold for scrap at $.03 per foot, how many packages of each size cable should Ajax make from a 30-foot spool?

Accepted Answer

​
Produce one package of 16 ft

Question 11

The return function for a shortest route problem refers to two directional arcs between nodes.

Accepted Answer

A) True 
 B)False

Question 12

​Explain the divide-and-conquer solution strategy of dynamic programming.

Accepted Answer

The divide-and-conquer solution strategy

Question 13

In order to use dynamic programming, one must be able to view the problem as a multistage decision problem.

Accepted Answer

A) True 
 B)False

Question 14

​A stage in a dynamic programming problem is defined when 2 variables and 2 functions related to that stage are defined. Identify and define the 2 variables and 2 functions and illustrate them with an example of your choice.

Accepted Answer

In a dynamic programming problem, a stag

Question 15

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.

Accepted Answer

The answer of A driver wants to make a trip...

Question 16

If x3 = t4(x4,d4) = x4 − 2d4 and r4(x4,d4) = 16d4, the stage transformation function is

Accepted Answer

A)  t 
B)  x 
C)  r 
D)  d 
A)  t 
B)  x 
C)  r 
D)  d

Question 17

If x3 = t4(x4,d4) = x4 − 2d4 and r4(x4,d4) = 16d4, the subscripts refer to

Accepted Answer

A)  state. 
B)  stage. 
C)  transformation. 
D)  return. 
A)  state. 
B)  stage. 
C)  transformation. 
D)  return.

Question 18

Dynamic programming is a general approach with stage decision problems differing substantially from application to application.

Accepted Answer

A) True 
 B)False

Question 19

​Unidyde Corporation is currently planning the production of red dye number 56 for the next four months. Production and handling costs, as well as production and storage capacity, vary from month to month. This data is given in the table below.
​
Production and holding costs are in ($1,000's per batch) and production levels and storage capacities are in batches. Holding costs are based on inventory on hand at the end of the month. The number of orders for batches the sales department has received over the four-month period are also given.
​   ​
Unidyne does not wish to have any inventory of the dye at the end of May. Its current inventory is 2 batches. Determine a production schedule for the next four months.
​

Accepted Answer

​
Produce 3 batches in Februar

Question 20

Solutions in dynamic programming

Accepted Answer

A)  are not optimal. 
B)  are unique. 
C)  represent each stage. 
D)  All of the alternatives are true. 
A)  are not optimal. 
B)  are unique. 
C)  represent each stage. 
D)  All of the alternatives are true.

Dynamic programming is a general approach rather than a specific technique.

Consider the following integer linear program Max 5x₁ + 7x₂ + 9x₃ s.t. 2x₁ + 3x₂ + 4x₃ ≤ 8 x₁ ≤ 3 x₂ ≤ 2 x₁, x₂, x₃ ≥ 0, integer a.Set up the network that represents the dynamic programming formulation. b.Solve the problem using dynamic programming.

The output of stage k is the input for stage k−1.

State variables in a shortest route problem represent

The stage transformation function identifies which state one reaches at the next stage for a given decision.

Dynamic programming must only involve a finite number of decision alternatives and a finite number of stages.

A return function is a value such as profit or loss associated with making decision d_n at:

Dynamic programming requires that its subproblems be independent of one another.

In solving a shortest route problem using dynamic programming the stages represent how many arcs you are from the terminal node.

The return function for a shortest route problem refers to two directional arcs between nodes.

Explain the divide-and-conquer solution strategy of dynamic programming.

In order to use dynamic programming, one must be able to view the problem as a multistage decision problem.

A stage in a dynamic programming problem is defined when 2 variables and 2 functions related to that stage are defined. Identify and define the 2 variables and 2 functions and illustrate them with an example of your choice.

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.

If x₃ = t₄(x₄,d₄) = x₄ − 2d₄ and r₄(x₄,d₄) = 16d₄, the stage transformation function is

If x₃ = t₄(x₄,d₄) = x₄ − 2d₄ and r₄(x₄,d₄) = 16d₄, the subscripts refer to

Dynamic programming is a general approach with stage decision problems differing substantially from application to application.

Solutions in dynamic programming

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Filters

Exam 21: Dynamic Programming

Dynamic programming is a general approach rather than a specific technique.

Consider the following integer linear program Max 5x1 + 7x2 + 9x3 s.t. 2x1 + 3x2 + 4x3 ≤ 8 x1 ≤ 3 x2 ≤ 2 x1, x2, x3 ≥ 0, integer ​ a.Set up the network that represents the dynamic programming formulation. b.Solve the problem using dynamic programming.

The output of stage k is the input for stage k−1.

State variables in a shortest route problem represent

​The stage transformation function identifies which state one reaches at the next stage for a given decision.

Dynamic programming must only involve a finite number of decision alternatives and a finite number of stages.

A return function is a value such as profit or loss associated with making decision dn at:

Dynamic programming requires that its subproblems be independent of one another.

In solving a shortest route problem using dynamic programming the stages represent how many arcs you are from the terminal node.

The return function for a shortest route problem refers to two directional arcs between nodes.

​Explain the divide-and-conquer solution strategy of dynamic programming.

In order to use dynamic programming, one must be able to view the problem as a multistage decision problem.

​A stage in a dynamic programming problem is defined when 2 variables and 2 functions related to that stage are defined. Identify and define the 2 variables and 2 functions and illustrate them with an example of your choice.

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.

If x3 = t4(x4,d4) = x4 − 2d4 and r4(x4,d4) = 16d4, the stage transformation function is

If x3 = t4(x4,d4) = x4 − 2d4 and r4(x4,d4) = 16d4, the subscripts refer to

Dynamic programming is a general approach with stage decision problems differing substantially from application to application.

Solutions in dynamic programming

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Filters

Consider the following integer linear program Max 5x₁ + 7x₂ + 9x₃ s.t. 2x₁ + 3x₂ + 4x₃ ≤ 8 x₁ ≤ 3 x₂ ≤ 2 x₁, x₂, x₃ ≥ 0, integer a.Set up the network that represents the dynamic programming formulation. b.Solve the problem using dynamic programming.

The stage transformation function identifies which state one reaches at the next stage for a given decision.

A return function is a value such as profit or loss associated with making decision d_n at:

Explain the divide-and-conquer solution strategy of dynamic programming.

A stage in a dynamic programming problem is defined when 2 variables and 2 functions related to that stage are defined. Identify and define the 2 variables and 2 functions and illustrate them with an example of your choice.

If x₃ = t₄(x₄,d₄) = x₄ − 2d₄ and r₄(x₄,d₄) = 16d₄, the stage transformation function is

If x₃ = t₄(x₄,d₄) = x₄ − 2d₄ and r₄(x₄,d₄) = 16d₄, the subscripts refer to