Question 1

Algebraic methods such as the simplex method are used to solve

Accepted Answer

A) nonlinear programming problems. 
B) any size linear programming problem. 
C) programming problems under uncertainty. 
D) graphical models. 
A) nonlinear programming problems. 
B) any size linear programming problem. 
C) programming problems under uncertainty. 
D) graphical models. B

Question 2

A student in a Management Science class developed this initial tableau for a maximization problem and now wants to perform row operations to create the next tableau and check for an optimal solution.Create the next tableau.Is there an optimal solution?
​   ​
​

Accepted Answer

Second tableau Solution is not optimal.There is a positive c_j - z_j value.

Question 3

When a system of simultaneous equations has more variables than equations,there is a unique solution.

Accepted Answer

A) True 
 B)False  False

Question 4

The purpose of the tableau form is to provide a(n)

Accepted Answer

A) infeasible solution. 
B) optimal infeasible solution. 
C) initial basic feasible solution. 
D) degenerate solution. 
A) infeasible solution. 
B) optimal infeasible solution. 
C) initial basic feasible solution. 
D) degenerate solution.

Question 5

Whenever a system of simultaneous linear equations has more variables than equations,

Accepted Answer

A) it is a basic set. 
B) it is a feasible set. 
C) there is a unique solution. 
D) we can expect an infinite number of solutions. 
A) it is a basic set. 
B) it is a feasible set. 
C) there is a unique solution. 
D) we can expect an infinite number of solutions.

Question 6

The operations research analyst for a big manufacturing firm in Oregon developed the following variable definitions for an LP maximization problem she was working on.The company was trying to determine how many consoles of each model to produce next week given each console had to go through three production departments.She obtained the following optimal simplex tableau for the problem and wanted to interpret its meaning.Variable definitions:
xl = number of model 1 consoles produced
x2 = number of model 2 consoles produced
s1 = unused personnel hours in department 1
s2 = unused personnel hours in department 2
s3 = unused personnel hours in department 3
objective function = total profit on model 1 and model 2 consoles produced in the coming week
​
Optimal tableau   ​

Accepted Answer

​ Optimal solution: Produce 15 model 1 c

Question 7

A solution is optimal when all values in the cj − zj row of the simplex tableau are either zero or positive.

Accepted Answer

A) True 
 B)False

Question 8

If a variable is not in the basis,its value is 0.

Accepted Answer

A) True 
 B)False

Question 9

Artificial variables are added for the purpose of obtaining an initial basic feasible solution.

Accepted Answer

A) True 
 B)False

Question 10

Which of the following steps is included in the preparation of a linear programming problem for a solution using the simplex method?

Accepted Answer

A) Formulate the problem. 
B) Set up the standard form by adding slack and/or subtracting surplus variables. 
C) Set up the tableau form. 
D) All of these are correct. 
A) Formulate the problem. 
B) Set up the standard form by adding slack and/or subtracting surplus variables. 
C) Set up the tableau form. 
D) All of these are correct.

Question 11

Infeasibility can be recognized when the optimality criterion indicates that an optimal solution has been obtained,and one or more of the artificial variables remain in the solution at a positive value.

Accepted Answer

A) True 
 B)False

Question 12

A student in a Management Science class wants to perform row operations on this second tableau and complete the third tableau to see if it is optimal.If it is optimal,what is the optimal answer?
​   ​
​

Accepted Answer

​ Third tableau @#IMG-DLM& ​ Solution is

Question 13

Write the following problem in tableau form.Which variables would be in the initial basic solution?

Accepted Answer

​ @#IMG-DLM& The ini

Question 14

Infeasibility exists when one or more of the artificial variables

Accepted Answer

A) remain in the final solution as a negative value. 
B) remain in the final solution as a positive value. 
C) have been removed from the basis. 
D) remain in the basis. 
A) remain in the final solution as a negative value. 
B) remain in the final solution as a positive value. 
C) have been removed from the basis. 
D) remain in the basis.

Question 15

At each iteration of the simplex procedure,a new variable becomes basic and a currently basic variable becomes nonbasic,preserving the same number of basic variables and improving the value of the objective function.

Accepted Answer

A) True 
 B)False

Question 16

Write the following problem in tableau form.Which variables would be in the initial basis?

Accepted Answer

​ @#IMG-DLM& The ini

Question 17

The coefficient of an artificial variable in the objective function is zero.

Accepted Answer

A) True 
 B)False

Question 18

The purpose of row operations is to create a unit column for the entering variable while maintaining unit columns for the remaining basic variables.

Accepted Answer

A) True 
 B)False

Question 19

A basic solution and a basic feasible solution

Accepted Answer

A) are the same thing. 
B) differ in the number of variables allowed to be zero. 
C) describe interior points and exterior points,respectively. 
D) differ in their inclusion of nonnegativity restrictions. 
A) are the same thing. 
B) differ in the number of variables allowed to be zero. 
C) describe interior points and exterior points,respectively. 
D) differ in their inclusion of nonnegativity restrictions.

Question 20

If one or more of the basic variables in a linear program have a value of zero,

Accepted Answer

A) post-optimality analysis is required. 
B) their dual prices will be equal. 
C) converting the pivot element will break the tie. 
D) a condition of degeneracy is present. 
A) post-optimality analysis is required. 
B) their dual prices will be equal. 
C) converting the pivot element will break the tie. 
D) a condition of degeneracy is present.

Algebraic methods such as the simplex method are used to solve

A student in a Management Science class developed this initial tableau for a maximization problem and now wants to perform row operations to create the next tableau and check for an optimal solution.Create the next tableau.Is there an optimal solution?

When a system of simultaneous equations has more variables than equations,there is a unique solution.

The purpose of the tableau form is to provide a(n)

Whenever a system of simultaneous linear equations has more variables than equations,

A solution is optimal when all values in the c_j − z_j row of the simplex tableau are either zero or positive.

If a variable is not in the basis,its value is 0.

Artificial variables are added for the purpose of obtaining an initial basic feasible solution.

Which of the following steps is included in the preparation of a linear programming problem for a solution using the simplex method?

Infeasibility can be recognized when the optimality criterion indicates that an optimal solution has been obtained,and one or more of the artificial variables remain in the solution at a positive value.

A student in a Management Science class wants to perform row operations on this second tableau and complete the third tableau to see if it is optimal.If it is optimal,what is the optimal answer?

Write the following problem in tableau form.Which variables would be in the initial basic solution?

Infeasibility exists when one or more of the artificial variables

At each iteration of the simplex procedure,a new variable becomes basic and a currently basic variable becomes nonbasic,preserving the same number of basic variables and improving the value of the objective function.

Write the following problem in tableau form.Which variables would be in the initial basis?

The coefficient of an artificial variable in the objective function is zero.

The purpose of row operations is to create a unit column for the entering variable while maintaining unit columns for the remaining basic variables.

A basic solution and a basic feasible solution

If one or more of the basic variables in a linear program have a value of zero,

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

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and Forecasting

Markov Processes

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

Exam 17: Linear Programming: Simplex Method

Algebraic methods such as the simplex method are used to solve

A student in a Management Science class developed this initial tableau for a maximization problem and now wants to perform row operations to create the next tableau and check for an optimal solution.Create the next tableau.Is there an optimal solution? ​ ​ ​

When a system of simultaneous equations has more variables than equations,there is a unique solution.

The purpose of the tableau form is to provide a(n)

Whenever a system of simultaneous linear equations has more variables than equations,

A solution is optimal when all values in the cj − zj row of the simplex tableau are either zero or positive.

If a variable is not in the basis,its value is 0.

Artificial variables are added for the purpose of obtaining an initial basic feasible solution.

Which of the following steps is included in the preparation of a linear programming problem for a solution using the simplex method?

Infeasibility can be recognized when the optimality criterion indicates that an optimal solution has been obtained,and one or more of the artificial variables remain in the solution at a positive value.

A student in a Management Science class wants to perform row operations on this second tableau and complete the third tableau to see if it is optimal.If it is optimal,what is the optimal answer? ​ ​ ​

Write the following problem in tableau form.Which variables would be in the initial basic solution?

Infeasibility exists when one or more of the artificial variables

At each iteration of the simplex procedure,a new variable becomes basic and a currently basic variable becomes nonbasic,preserving the same number of basic variables and improving the value of the objective function.

Write the following problem in tableau form.Which variables would be in the initial basis?

The coefficient of an artificial variable in the objective function is zero.

The purpose of row operations is to create a unit column for the entering variable while maintaining unit columns for the remaining basic variables.

A basic solution and a basic feasible solution

If one or more of the basic variables in a linear program have a value of zero,

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

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and Forecasting

Markov Processes

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

A student in a Management Science class developed this initial tableau for a maximization problem and now wants to perform row operations to create the next tableau and check for an optimal solution.Create the next tableau.Is there an optimal solution?

A solution is optimal when all values in the c_j − z_j row of the simplex tableau are either zero or positive.

A student in a Management Science class wants to perform row operations on this second tableau and complete the third tableau to see if it is optimal.If it is optimal,what is the optimal answer?