Question 1

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. B

Question 2

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. C

Question 3

The owner of a small construction firm is excavating at three sites. He wishes to assign his 5 additional trucks in such a way as to minimize his total costs. Each site can use 0 to 3 additional trucks; no site can use more than 3 trucks efficiently. The following site total costs are known. $$\begin{array} { c | r c c } 
\text { Number } && { \text { Cost of Excavating } } \
\text { of Trucks }& \text { Site 1 }& \text { Site 2 }& \text { Site 3 }\
\hline 0 & \$ 10000 & \$ 15000 & \$ 20000  \
 1 & 10000 & 14000 & 18000 \
2 & 9200 & 13250 & 17500 \
3 & 8500 & 12750 & 17250
\end{array}$$ 
a.Use dynamic programming to find the assignment of the additional trucks that minimizes total cost.
b.If the owner had only 4 trucks to assign, what would be the optimal assignment and total cost?

Accepted 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.

Question 4

Define the following terms as they relate to dynamic programming.
a.Stage.
b.State variable.
c.Stage transformation function.

Accepted Answer

The answer of Define the following terms as they relate...

Question 5

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 6

The solution of stage k of a dynamic programming problem is dependent upon the solution of stage k-1.

Accepted Answer

A) True 
 B)False

Question 7

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

Accepted Answer

A) True 
 B)False

Question 8

Stage transformation functions

Accepted Answer

A) are linear. 
B) calculate the return. 
C) determine the output of the stage. 
D) All of the alternatives are true. 
A) are linear. 
B) calculate the return. 
C) determine the output of the stage. 
D) All of the alternatives are true.

Question 9

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 10

Stages of a dynamic programming solution procedure

Accepted Answer

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 the alternatives are true. 
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 the alternatives are true.

Question 11

If x3 = t4 (x4,d4) = x4 -2d4 and r4(x4,d4) = 16d4 the state variable is

Accepted Answer

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

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

What is the Principle of Optimality, and what is its relationship to Dynamic Programming?

Accepted Answer

The Principle of Optimality states that

Question 14

We have a number of types of items to be shipped as cargo. The total available weight in the truck is ten tons. We wish to determine the number of units of items to be shipped to maximize profit. $$\begin{array} { c c c } 
\text { Item } & \text { Weight (Tons) } & \text { Profit (1000s dollars) } \
\text { A } & 3 & 5 \
\text { B } & 4 & 7 \
\text { C } & 2 & 3
\end{array}$$

Accepted Answer

Ship 0 tons of item

Question 15

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 16

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. $$\begin{array} { c | c c c c c c c } 
\text { From } & & { \text { To City: } } \
\text { City: } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline 1 & - & 2 & 2 & 4 & - & - & - \
2 & - & - & - & - & -4 & 10 & - \
3 & - & - & - & - & 12 & 6 & - \
4 & - & - & - & - & 10 & - & - \
5 & - & - & - & - & - & - & 14 \
6 & - & - & - & - & - & - & 2 \
7 & - & - & - & - & - & - & -
\end{array}$$

Accepted Answer

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

Question 17

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 18

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

Accepted Answer

a. @#IMG-DLM& b.x₁ =

Question 19

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 20

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

Accepted Answer

A) True 
 B)False

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

Solutions in dynamic programming

Define the following terms as they relate to dynamic programming. a.Stage. b.State variable. c.Stage transformation function.

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

The solution of stage k of a dynamic programming problem is dependent upon the solution of stage k-1.

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

Stage transformation functions

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.

Stages of a dynamic programming solution procedure

If x₃ = t₄(x₄,d₄) = x₄ -2d₄ and r₄(x₄,d₄) = 16d₄ the state variable is

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

What is the Principle of Optimality, and what is its relationship to Dynamic Programming?

We have a number of types of items to be shipped as cargo. The total available weight in the truck is ten tons. We wish to determine the number of units of items to be shipped to maximize profit. Item Weight (Tons) Profit (1000s dollars) A 3 5 B 4 7 C 2 3

State variables in a shortest route problem represent

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. From To City: 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 - - - - - - -

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

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

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

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

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 Problems

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

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

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

Solutions in dynamic programming

Define the following terms as they relate to dynamic programming. a.Stage. b.State variable. c.Stage transformation function.

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

The solution of stage k of a dynamic programming problem is dependent upon the solution of stage k-1.

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

Stage transformation functions

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.

Stages of a dynamic programming solution procedure

If x3 = t4 (x4,d4) = x4 -2d4 and r4(x4,d4) = 16d4 the state variable is

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

What is the Principle of Optimality, and what is its relationship to Dynamic Programming?

We have a number of types of items to be shipped as cargo. The total available weight in the truck is ten tons. We wish to determine the number of units of items to be shipped to maximize profit. Item Weight (Tons) Profit (1000s dollars) A 3 5 B 4 7 C 2 3

State variables in a shortest route problem represent

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. From To City: 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 - - - - - - -

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

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

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

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

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 Problems

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Filters

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

If x₃ = t₄(x₄,d₄) = x₄ -2d₄ and r₄(x₄,d₄) = 16d₄ the state variable is

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

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

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