Question 1

To perform sensitivity analysis involving an integer linear program, it is recommended to

Accepted Answer

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. 
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.

Question 2

In a model involving fixed costs, the 0 - 1 variable guarantees that the capacity is not available unless the cost has been incurred.

Accepted Answer

A) True 
 B)False

Question 3

Let x1 , x2 , and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1).Which answer below indicates that at least two of the projects must be done?

Accepted Answer

A) x1 + x2 + x3 > 2 
B) x1 + x2 + x3 1 + x2 + x3 = 2 
D) x1 - x2 = 0 
A) x1 + x2 + x3 > 2 
B) x1 + x2 + x3 1 + x2 + x3 = 2 
D) x1 - x2 = 0

Question 4

If x1 + x2 1 and y1 is 0 - 1, then if y1 is 0, x1 and x2 will be 0.

Accepted Answer

A) True 
 B)False

Question 5

In an all-integer linear program,

Accepted Answer

A) all objective function coefficients must be integer. 
B) all right-hand side values must be integer. 
C) all variables must be integer. 
D) all objective function coefficients and right-hand side values must be integer. 
A) all objective function coefficients must be integer. 
B) all right-hand side values must be integer. 
C) all variables must be integer. 
D) all objective function coefficients and right-hand side values must be integer.

Question 6

The product design and market share optimization problem presented in the textbook is formulated as a 0-1 integer linear programming model.

Accepted Answer

A) True 
 B)False

Question 7

Some linear programming problems have a special structure which guarantees that the variables will have integer values.

Accepted Answer

A) True 
 B)False

Question 8

The solution to the LP Relaxation of a maximization integer linear program provides

Accepted Answer

A) an upper bound for the value of the objective function. 
B) a lower bound for the value of the objective function. 
C) an upper bound for the value of the decision variables 
D) a lower bound for the value of the decision variables 
A) an upper bound for the value of the objective function. 
B) a lower bound for the value of the objective function. 
C) an upper bound for the value of the decision variables 
D) a lower bound for the value of the decision variables

Question 9

Rounding the solution of an LP Relaxation to the nearest integer values provides

Accepted Answer

A) a feasible but not necessarily optimal integer solution. 
B) an integer solution that is optimal. 
C) an integer solution that might be neither feasible nor optimal. 
D) an infeasible solution. 
A) a feasible but not necessarily optimal integer solution. 
B) an integer solution that is optimal. 
C) an integer solution that might be neither feasible nor optimal. 
D) an infeasible solution.

Question 10

The graph of a problem that requires x1 and x2 to be integer has a feasible region

Accepted Answer

A) the same as its LP relaxation. 
B) of dots. 
C) of horizontal stripes. 
D) of vertical stripes. 
A) the same as its LP relaxation. 
B) of dots. 
C) of horizontal stripes. 
D) of vertical stripes.

To perform sensitivity analysis involving an integer linear program, it is recommended to

In a model involving fixed costs, the 0 - 1 variable guarantees that the capacity is not available unless the cost has been incurred.

Let x₁ , x₂ , and x₃ be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1).Which answer below indicates that at least two of the projects must be done?

If x₁ + x₂ < 500y₁ and y₁ is 0 - 1, then if y₁ is 0, x₁ and x₂ will be 0.

In an all-integer linear program,

The product design and market share optimization problem presented in the textbook is formulated as a 0-1 integer linear programming model.

Some linear programming problems have a special structure which guarantees that the variables will have integer values.

The solution to the LP Relaxation of a maximization integer linear program provides

Rounding the solution of an LP Relaxation to the nearest integer values provides

The graph of a problem that requires x₁ and x₂ to be integer has a feasible region

Introduction

Introduction to Linear Programming

LP Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications

Advanced Linear Programming Applications

Distribution and Network Problems

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

Markov Processes

LP: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

Exam 7: Integer Linear Programming

To perform sensitivity analysis involving an integer linear program, it is recommended to

In a model involving fixed costs, the 0 - 1 variable guarantees that the capacity is not available unless the cost has been incurred.

Let x1 , x2 , and x3 be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1).Which answer below indicates that at least two of the projects must be done?

If x1 + x2 < 500y1 and y1 is 0 - 1, then if y1 is 0, x1 and x2 will be 0.

In an all-integer linear program,

The product design and market share optimization problem presented in the textbook is formulated as a 0-1 integer linear programming model.

Some linear programming problems have a special structure which guarantees that the variables will have integer values.

The solution to the LP Relaxation of a maximization integer linear program provides

Rounding the solution of an LP Relaxation to the nearest integer values provides

The graph of a problem that requires x1 and x2 to be integer has a feasible region

Introduction

Introduction to Linear Programming

LP Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications

Advanced Linear Programming Applications

Distribution and Network Problems

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

Markov Processes

LP: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

Let x₁ , x₂ , and x₃ be 0 - 1 variables whose values indicate whether the projects are not done (0) or are done (1).Which answer below indicates that at least two of the projects must be done?

If x₁ + x₂ < 500y₁ and y₁ is 0 - 1, then if y₁ is 0, x₁ and x₂ will be 0.

The graph of a problem that requires x₁ and x₂ to be integer has a feasible region