Question 1

The standard form of a linear programming problem will have the same solution as the original problem.

Accepted Answer

A) True 
 B)False  True

Question 2

The improvement in the value of the objective function per unit increase in a right-hand side is the

Accepted Answer

A) sensitivity value. 
B) dual price. 
C) constraint coefficient. 
D) slack value. 
A) sensitivity value. 
B) dual price. 
C) constraint coefficient. 
D) slack value. B

Question 3

​Explain how to graph the line x1 − 2x2 ≥ 0.

Accepted Answer

To graph the line x - 2x ≥ 0, we first need to simplify the inequality.

Combining like terms, we get -x ≥ 0.

To graph this inequality, we can start by graphing the line y = -x. This line has a slope of -1 and a y-intercept of 0.

Since the inequality is -x ≥ 0, we want to shade the region where y is less than or equal to 0. This means we shade the area below the line y = -x.

So, the graph of the inequality x - 2x ≥ 0 is the region below the line y = -x.

Question 4

Which of the following statements is NOT true?

Accepted Answer

A) A feasible solution satisfies all constraints. 
B) An optimal solution satisfies all constraints. 
C) An infeasible solution violates all constraints. 
D) A feasible solution point does not have to lie on the boundary of the feasible region. 
A) A feasible solution satisfies all constraints. 
B) An optimal solution satisfies all constraints. 
C) An infeasible solution violates all constraints. 
D) A feasible solution point does not have to lie on the boundary of the feasible region.

Question 5

Because the dual price represents the improvement in the value of the optimal solution per unit increase in right-hand-side,a dual price cannot be negative.

Accepted Answer

A) True 
 B)False

Question 6

All of the following statements about a redundant constraint are correct EXCEPT

Accepted Answer

A) A redundant constraint does not affect the optimal solution. 
B) A redundant constraint does not affect the feasible region. 
C) Recognizing a redundant constraint is easy with the graphical solution method. 
D) At the optimal solution,a redundant constraint will have zero slack. 
A) A redundant constraint does not affect the optimal solution. 
B) A redundant constraint does not affect the feasible region. 
C) Recognizing a redundant constraint is easy with the graphical solution method. 
D) At the optimal solution,a redundant constraint will have zero slack.

Question 7

​Create a linear programming problem with two decision variables and three constraints that will include both a slack
and a surplus variable in standard form.Write your problem in standard form.

Accepted Answer

The linear programming problem with two

Question 8

The corner points of the feasible region represent alternative optimal solutions.
​

Accepted Answer

A) True 
 B)False

Question 9

A redundant constraint is a binding constraint.

Accepted Answer

A) True 
 B)False

Question 10

Which of the following special cases does not require reformulation of the problem in order to obtain a solution?

Accepted Answer

A) alternate optimality 
B) infeasibility 
C) unboundedness 
D) each case requires a reformulation. 
A) alternate optimality 
B) infeasibility 
C) unboundedness 
D) each case requires a reformulation.

Question 11

Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution.

Accepted Answer

A) True 
 B)False

Question 12

As long as the slope of the objective function stays between the slopes of the binding constraints

Accepted Answer

A) the value of the objective function won't change. 
B) there will be alternative optimal solutions. 
C) the values of the dual variables won't change. 
D) there will be no slack in the solution. 
A) the value of the objective function won't change. 
B) there will be alternative optimal solutions. 
C) the values of the dual variables won't change. 
D) there will be no slack in the solution.

Question 13

In a linear programming problem,the objective function and the constraints must be linear functions of the decision variables.

Accepted Answer

A) True 
 B)False

Question 14

​The three assumptions necessary for a linear programming model to be appropriate include all of the following except

Accepted Answer

A) ​proportionality 
B) ​additivity 
C) ​divisibility 
D) ​normality 
A) ​proportionality 
B) ​additivity 
C) ​divisibility 
D) ​normality

Question 15

To find the optimal solution to a linear programming problem using the graphical method

Accepted Answer

A) find the feasible point that is the farthest away from the origin. 
B) find the feasible point that is at the highest location. 
C) find the feasible point that is closest to the origin. 
D) None of the alternatives is correct. 
A) find the feasible point that is the farthest away from the origin. 
B) find the feasible point that is at the highest location. 
C) find the feasible point that is closest to the origin. 
D) None of the alternatives is correct.

Question 16

​Explain the steps of the graphical solution procedure for a minimization problem.

Accepted Answer

The graphical solution procedure for a m

Question 17

No matter what value it has,each objective function line is parallel to every other objective function line in a problem.

Accepted Answer

A) True 
 B)False

Question 18

It is possible to have exactly two optimal solutions to a linear programming problem.

Accepted Answer

A) True 
 B)False

Question 19

​Explain the concepts of proportionality,additivity,and divisibility.

Accepted Answer

Proportionality refers to the relationsh

Question 20

Which of the following is a valid objective function for a linear programming problem?

Accepted Answer

A) Max 5xy 
B) Min 4x + 3y + (2/3)z 
C) Max 5x2 + 6y2 
D) Min (x1 + x2)/x3 
A) Max 5xy 
B) Min 4x + 3y + (2/3)z 
C) Max 5x2 + 6y2 
D) Min (x1 + x2)/x3

The standard form of a linear programming problem will have the same solution as the original problem.

The improvement in the value of the objective function per unit increase in a right-hand side is the

Explain how to graph the line x₁ − 2x₂ ≥ 0.

Which of the following statements is NOT true?

Because the dual price represents the improvement in the value of the optimal solution per unit increase in right-hand-side,a dual price cannot be negative.

All of the following statements about a redundant constraint are correct EXCEPT

Create a linear programming problem with two decision variables and three constraints that will include both a slack and a surplus variable in standard form.Write your problem in standard form.

The corner points of the feasible region represent alternative optimal solutions.

A redundant constraint is a binding constraint.

Which of the following special cases does not require reformulation of the problem in order to obtain a solution?

Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution.

As long as the slope of the objective function stays between the slopes of the binding constraints

In a linear programming problem,the objective function and the constraints must be linear functions of the decision variables.

The three assumptions necessary for a linear programming model to be appropriate include all of the following except

To find the optimal solution to a linear programming problem using the graphical method

Explain the steps of the graphical solution procedure for a minimization problem.

No matter what value it has,each objective function line is parallel to every other objective function line in a problem.

It is possible to have exactly two optimal solutions to a linear programming problem.

Explain the concepts of proportionality,additivity,and divisibility.

Which of the following is a valid objective function for a linear programming problem?

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility Game Theory

Time Series Analysis Forecasting

LP Sensitivity Analysis

LP Applications

Distribution Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

Exam 7: Intro to Linear Programming

The standard form of a linear programming problem will have the same solution as the original problem.

The improvement in the value of the objective function per unit increase in a right-hand side is the

​Explain how to graph the line x1 − 2x2 ≥ 0.

Which of the following statements is NOT true?

Because the dual price represents the improvement in the value of the optimal solution per unit increase in right-hand-side,a dual price cannot be negative.

All of the following statements about a redundant constraint are correct EXCEPT

​Create a linear programming problem with two decision variables and three constraints that will include both a slack and a surplus variable in standard form.Write your problem in standard form.

The corner points of the feasible region represent alternative optimal solutions. ​

A redundant constraint is a binding constraint.

Which of the following special cases does not require reformulation of the problem in order to obtain a solution?

Increasing the right-hand side of a nonbinding constraint will not cause a change in the optimal solution.

As long as the slope of the objective function stays between the slopes of the binding constraints

In a linear programming problem,the objective function and the constraints must be linear functions of the decision variables.

​The three assumptions necessary for a linear programming model to be appropriate include all of the following except

To find the optimal solution to a linear programming problem using the graphical method

​Explain the steps of the graphical solution procedure for a minimization problem.

No matter what value it has,each objective function line is parallel to every other objective function line in a problem.

It is possible to have exactly two optimal solutions to a linear programming problem.

​Explain the concepts of proportionality,additivity,and divisibility.

Which of the following is a valid objective function for a linear programming problem?

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility Game Theory

Time Series Analysis Forecasting

LP Sensitivity Analysis

LP Applications

Distribution Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

Explain how to graph the line x₁ − 2x₂ ≥ 0.

Create a linear programming problem with two decision variables and three constraints that will include both a slack and a surplus variable in standard form.Write your problem in standard form.

The corner points of the feasible region represent alternative optimal solutions.

The three assumptions necessary for a linear programming model to be appropriate include all of the following except

Explain the steps of the graphical solution procedure for a minimization problem.

Explain the concepts of proportionality,additivity,and divisibility.