Question 1

The 0-1 variables in the fixed cost models correspond to

Accepted Answer

A) a process for which a fixed cost occurs. 
B) the number of products produced. 
C) the number of units produced. 
D) the actual value of the fixed cost. 
A) a process for which a fixed cost occurs. 
B) the number of products produced. 
C) the number of units produced. 
D) the actual value of the fixed cost. A

Question 2

A multiple choice constraint involves selecting k out of n alternatives, where k > 2.

Accepted Answer

A) True 
 B)False  False

Question 3

The constraint x1 - x2 = 0 implies that if project 1 is selected, project 2 cannot be.

Accepted Answer

A) True 
 B)False  False

Question 4

Rounded solutions to linear programs must be evaluated for

Accepted Answer

A) feasibility and optimality. 
B) sensitivity and duality. 
C) relaxation and boundedness. 
D) each of the above is true. 
A) feasibility and optimality. 
B) sensitivity and duality. 
C) relaxation and boundedness. 
D) each of the above is true.

Question 5

Let x1 and x2 be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done.Which answer below indicates that project 2 can be done only if project 1 is done?

Accepted Answer

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

Question 6

The constraint x1 + x2 + x3 + x4 < 2 means that two out of the first four projects must be selected.

Accepted Answer

A) True 
 B)False

Question 7

If the acceptance of project A is conditional on the acceptance of project B, and vice versa, the appropriate constraint to use is a

Accepted Answer

A) multiple-choice constraint. 
B) k out of n alternatives constraint. 
C) mutually exclusive constraint. 
D) corequisite constraint. 
A) multiple-choice constraint. 
B) k out of n alternatives constraint. 
C) mutually exclusive constraint. 
D) corequisite constraint.

Question 8

Most practical applications of integer linear programming involve

Accepted Answer

A) only 0-1 integer variables and not ordinary integer variables. 
B) mostly ordinary integer variables and a small number of 0-1 integer variables. 
C) only ordinary integer variables. 
D) a near equal number of ordinary integer variables and 0-1 integer variables. 
A) only 0-1 integer variables and not ordinary integer variables. 
B) mostly ordinary integer variables and a small number of 0-1 integer variables. 
C) only ordinary integer variables. 
D) a near equal number of ordinary integer variables and 0-1 integer variables.

Question 9

If a problem has only less-than-or-equal-to constraints with positive coefficients for the variables, rounding down will always provide a feasible integer solution.

Accepted Answer

A) True 
 B)False

Question 10

Which of the following is the most useful contribution of integer programming?

Accepted Answer

A) finding whole number solutions where fractional solutions would not be appropriate 
B) using 0-1 variables for modeling flexibility 
C) increased ease of solution 
D) provision for solution procedures for transportation and assignment problems 
A) finding whole number solutions where fractional solutions would not be appropriate 
B) using 0-1 variables for modeling flexibility 
C) increased ease of solution 
D) provision for solution procedures for transportation and assignment problems

Question 11

The solution to the LP Relaxation of a minimization problem will always be less than or equal to the value of the integer program minimization problem.

Accepted Answer

A) True 
 B)False

Question 12

If the optimal solutionASW8 to the LP relaxation problem is integer, it is the optimal solution to the integer linear program.

Accepted Answer

A) True 
 B)False

Question 13

The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will maximize the number of sampled customers preferring the brand in question.

Accepted Answer

A) True 
 B)False

Question 14

The LP Relaxation contains the objective function and constraints of the IP problem, but drops all integer restrictions.

Accepted Answer

A) True 
 B)False

Question 15

In a model, x1 > 0 and integer, x2 > 0, and x3 = 0, 1.Which solution would not be feasible?

Accepted Answer

A) x1 = 5, x2 = 3, x3 = 0 
B) x1 = 4, x2 = .389, x3 = 1 
C) x1 = 2, x2 = 3, x3 = .578 
D) x1 = 0, x2 = 8, x3 = 0 
A) x1 = 5, x2 = 3, x3 = 0 
B) x1 = 4, x2 = .389, x3 = 1 
C) x1 = 2, x2 = 3, x3 = .578 
D) x1 = 0, x2 = 8, x3 = 0

Question 16

Dual prices cannot be used for integer programming sensitivity analysis because they are designed for linear programs.

Accepted Answer

A) True 
 B)False

Question 17

In general, rounding large values of decision variables to the nearest integer value causes fewer problems than rounding small values.

Accepted Answer

A) True 
 B)False

Question 18

Slack and surplus variables are not useful in integer linear programs.

Accepted Answer

A) True 
 B)False

Question 19

Sensitivity analysis for integer linear programming

Accepted Answer

A) can be provided only by computer. 
B) has precisely the same interpretation as that from linear programming. 
C) does not have the same interpretation and should be disregarded. 
D) is most useful for 0 - 1 models. 
A) can be provided only by computer. 
B) has precisely the same interpretation as that from linear programming. 
C) does not have the same interpretation and should be disregarded. 
D) is most useful for 0 - 1 models.

Question 20

Modeling a fixed cost problem as an integer linear program requires

Accepted Answer

A) adding the fixed costs to the corresponding variable costs in the objective function. 
B) using 0-1 variables. 
C) using multiple-choice constraints. 
D) using LP relaxation. 
A) adding the fixed costs to the corresponding variable costs in the objective function. 
B) using 0-1 variables. 
C) using multiple-choice constraints. 
D) using LP relaxation.

Exam 7: Integer Linear Programming

The 0-1 variables in the fixed cost models correspond to

A multiple choice constraint involves selecting k out of n alternatives, where k > 2.

The constraint x1 - x2 = 0 implies that if project 1 is selected, project 2 cannot be.

Rounded solutions to linear programs must be evaluated for

Let x1 and x2 be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done.Which answer below indicates that project 2 can be done only if project 1 is done?

The constraint x1 + x2 + x3 + x4 < 2 means that two out of the first four projects must be selected.

If the acceptance of project A is conditional on the acceptance of project B, and vice versa, the appropriate constraint to use is a

Most practical applications of integer linear programming involve

If a problem has only less-than-or-equal-to constraints with positive coefficients for the variables, rounding down will always provide a feasible integer solution.

Which of the following is the most useful contribution of integer programming?

The solution to the LP Relaxation of a minimization problem will always be less than or equal to the value of the integer program minimization problem.

If the optimal solutionASW8 to the LP relaxation problem is integer, it is the optimal solution to the integer linear program.

The objective of the product design and market share optimization problem presented in the textbook is to choose the levels of each product attribute that will maximize the number of sampled customers preferring the brand in question.

The LP Relaxation contains the objective function and constraints of the IP problem, but drops all integer restrictions.

In a model, x1 > 0 and integer, x2 > 0, and x3 = 0, 1.Which solution would not be feasible?

Dual prices cannot be used for integer programming sensitivity analysis because they are designed for linear programs.

In general, rounding large values of decision variables to the nearest integer value causes fewer problems than rounding small values.

Slack and surplus variables are not useful in integer linear programs.

Sensitivity analysis for integer linear programming

Modeling a fixed cost problem as an integer linear program requires

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

The constraint x₁ - x₂ = 0 implies that if project 1 is selected, project 2 cannot be.

Let x₁ and x₂ be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done.Which answer below indicates that project 2 can be done only if project 1 is done?

The constraint x₁ + x₂ + x₃ + x₄ < 2 means that two out of the first four projects must be selected.

In a model, x₁ > 0 and integer, x₂ > 0, and x₃ = 0, 1.Which solution would not be feasible?