Question 1

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 2

To perform sensitivity analysis involving an integer linear program,it is best 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 3

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 4

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 5

Market Pulse Research has conducted a study for Lucas Furniture on some designs for a new commercial office desk.Three attributes were found to be most influential in determining which desk is most desirable: number of file drawers,the presence or absence of pullout writing boards,and simulated wood or solid color finish.Listed below are the part-worths for each level of each attribute provided by a sample of seven potential Lucas customers.​   ​
Suppose the overall utility (sum of part-worths)of the current favorite commercial office desk is 50 for each customer.What product design will maximize the share of choices for the seven sample participants? Using Excel,formulate and solve this 0-1 integer programming problem.

Accepted Answer

Define the decision variables:There are

Question 6

Solve the following problem graphically.   ​ 
a.Graph the constraints for this problem.Indicate all feasible solutions.
b.Find the optimal solution to the LP Relaxation.Round down to find a feasible integer solution.Is this solution optimal?
c.Find the optimal solution.
​

Accepted Answer

​ a. The feasible region consists of the

Question 7

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 8

If project 5 must be completed before project 6,the constraint would be x5 − x6 ≤ 0.

Accepted Answer

A) True 
 B)False

Question 9

Your express package courier company is drawing up new zones for the location of drop boxes for customers.The city has been divided into seven zones.You have targeted six possible locations for drop boxes.The list of the seven zones and which drop boxes could be reached easily from each zone is listed below.   ​
Let xi = 1 if drop box location i is used,0 otherwise.Develop a model to provide the smallest number of locations,but make sure that each zone is covered by at least two boxes.​

Accepted Answer

Question 10

Rounding the solution of an LP Relaxation to the nearest integer values provides a(n)

Accepted Answer

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

Question 11

Which of the following applications modeled in the textbook does NOT involve only 0-1 integer variables?

Accepted Answer

A) supply chain design 
B) bank location 
C) capital budgeting 
D) product design and market share optimization 
A) supply chain design 
B) bank location 
C) capital budgeting 
D) product design and market share optimization

Question 12

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.

Question 13

The computer output for integer programs in the textbook does not include reduced costs,dual values,or sensitivity ranges because these variables are not meaningful for integer programs.​

Accepted Answer

A) True 
 B)False

Question 14

Let x1 and x2 be 0-1 variables whose values indicate whether projects 1 and 2 are/are not done.Which of the following answers 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 ≤ 0 
D) x1 − x2 ≥ 0 
A) x1 + x2 = 1 
B) x1 + x2 = 2 
C) x1 − x2 ≤ 0 
D) x1 − x2 ≥ 0

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

If the optimal solution to the LP Relaxation problem is an integer,it is the optimal solution to the integer linear program.

Accepted Answer

A) True 
 B)False

Question 17

Given the following all-integer linear program:
​
Max 15x1 + 2x2
s.t. 7x1 + x2 1 - x2 1,x2 > 0 and integer
​
a.Solve the problem as an LP,ignoring the integer constraints.
b.What solution is obtained by rounding up fractions greater than or equal to 1/2? Is this the optimal integer solution?
c.What solution is obtained by rounding down all fractions? Is this the optimal integer solution? Explain.
d.Show that the optimal objective function value for the ILP (integer linear programming)is lower than that for the optimal LP.
e.Why is the optimal objective function value for the ILP problem always less than or equal to the corresponding LP's optimal objective function value? When would they be equal? Comment on the optimal objective function of the MILP (mixed-integer linear programming)compared to the corresponding LP and ILP.

Accepted Answer

a.x₁ = 2.8,x₂ = 3.4,Obj.function = 48.8

Question 18

In a model,x1 ≥ 0 and integer,x2 ≥ 0,and x3 = 0,1.Which of the following solutions would NOT be feasible?

Accepted Answer

A) x1 = 5,x2 = 3,x3 = 0 
B) x1 = 4,x2 = 0.389,x3 = 1 
C) x1 = 2,x2 = 3,x3 = 0.578 
D) x1 = 0,x2 = 8,x3 = 0 
A) x1 = 5,x2 = 3,x3 = 0 
B) x1 = 4,x2 = 0.389,x3 = 1 
C) x1 = 2,x2 = 3,x3 = 0.578 
D) x1 = 0,x2 = 8,x3 = 0

Question 19

Integer linear programs provide substantial modeling flexibility and thus are harder to solve than linear programs.​

Accepted Answer

A) True 
 B)False

Question 20

Grush Consulting has five projects to consider.Each will require time in the next two quarters according to the table below.   ​
Revenue from each project is also shown.Develop a model whose solution would maximize revenue,meet the time budget of 25 in the first quarter and 20 in the second quarter,and not do both projects C and D.

Accepted Answer

Let A = 1 if project

In an all-integer linear program,

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

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

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.

Solve the following problem graphically. a.Graph the constraints for this problem.Indicate all feasible solutions. b.Find the optimal solution to the LP Relaxation.Round down to find a feasible integer solution.Is this solution optimal? c.Find the optimal solution.

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

If project 5 must be completed before project 6,the constraint would be x₅ − x₆ ≤ 0.

Rounding the solution of an LP Relaxation to the nearest integer values provides a(n)

Which of the following applications modeled in the textbook does NOT involve only 0-1 integer variables?

Modeling a fixed cost problem as an integer linear program requires

The computer output for integer programs in the textbook does not include reduced costs,dual values,or sensitivity ranges because these variables are not meaningful for integer programs.

Let x1 and x2 be 0-1 variables whose values indicate whether projects 1 and 2 are/are not done.Which of the following answers indicates that project 2 can be done only if project 1 is done?

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

If the optimal solution to the LP Relaxation problem is an integer,it is the optimal solution to the integer linear program.

In a model,x₁ ≥ 0 and integer,x₂ ≥ 0,and x₃ = 0,1.Which of the following solutions would NOT be feasible?

Integer linear programs provide substantial modeling flexibility and thus are harder to solve than linear programs.

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, finance, and OM

Advanced Linear Programming Applications

Distribution and Network Models

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

Dynamic Programming

Filters

Exam 7: Integer Linear Programming

In an all-integer linear program,

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

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

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.

Solve the following problem graphically. ​ a.Graph the constraints for this problem.Indicate all feasible solutions. b.Find the optimal solution to the LP Relaxation.Round down to find a feasible integer solution.Is this solution optimal? c.Find the optimal solution. ​

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

If project 5 must be completed before project 6,the constraint would be x5 − x6 ≤ 0.

Rounding the solution of an LP Relaxation to the nearest integer values provides a(n)

Which of the following applications modeled in the textbook does NOT involve only 0-1 integer variables?

Modeling a fixed cost problem as an integer linear program requires

The computer output for integer programs in the textbook does not include reduced costs,dual values,or sensitivity ranges because these variables are not meaningful for integer programs.​

Let x1 and x2 be 0-1 variables whose values indicate whether projects 1 and 2 are/are not done.Which of the following answers indicates that project 2 can be done only if project 1 is done?

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

If the optimal solution to the LP Relaxation problem is an integer,it is the optimal solution to the integer linear program.

In a model,x1 ≥ 0 and integer,x2 ≥ 0,and x3 = 0,1.Which of the following solutions would NOT be feasible?

Integer linear programs provide substantial modeling flexibility and thus are harder to solve than linear programs.​

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, finance, and OM

Advanced Linear Programming Applications

Distribution and Network Models

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

Dynamic Programming

Filters

Solve the following problem graphically. a.Graph the constraints for this problem.Indicate all feasible solutions. b.Find the optimal solution to the LP Relaxation.Round down to find a feasible integer solution.Is this solution optimal? c.Find the optimal solution.

If project 5 must be completed before project 6,the constraint would be x₅ − x₆ ≤ 0.

The computer output for integer programs in the textbook does not include reduced costs,dual values,or sensitivity ranges because these variables are not meaningful for integer programs.

In a model,x₁ ≥ 0 and integer,x₂ ≥ 0,and x₃ = 0,1.Which of the following solutions would NOT be feasible?

Integer linear programs provide substantial modeling flexibility and thus are harder to solve than linear programs.