Question 1

We recognize infeasibility when one or more of the artificial variables do not remain in the solution at a positive value.

Accepted Answer

A) True 
 B)False  False

Question 2

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. B

Question 3

Which of the following is not a step that is necessary to prepare a linear programming problem for 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) perform elementary row and column operations 
D) set up the tableau form 
A) formulate the problem. 
B) set up the standard form by adding slack and/or subtracting surplus variables. 
C) perform elementary row and column operations 
D) set up the tableau form C

Question 4

When a set of simultaneous equations has more variables than constraints,

Accepted Answer

A) it is a basic set. 
B) it is a feasible set. 
C) there is a unique solution. 
D) there are many solutions. 
A) it is a basic set. 
B) it is a feasible set. 
C) there is a unique solution. 
D) there are many solutions.

Question 5

The variable to enter into the basis is the variable with the largest positive cj - zj value.

Accepted Answer

A) True 
 B)False

Question 6

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 7

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

Accepted Answer

A) True 
 B)False

Question 8

Every extreme point of the graph of a two variable linear programming problem is a basic feasible solution.

Accepted Answer

A) True 
 B)False

Question 9

A basic feasible solution satisfies the nonnegativity restriction.

Accepted Answer

A) True 
 B)False

Question 10

An alternative optimal solution is indicated when in the simplex tableau

Accepted Answer

A) a non-basic variable has a value of zero in the cj - zj row. 
B) a basic variable has a positive value in the cj - zj row. 
C) a basic variable has a value of zero in the cj - zj row. 
D) a non-basic variable has a positive value in the cj - zj row. 
A) a non-basic variable has a value of zero in the cj - zj row. 
B) a basic variable has a positive value in the cj - zj row. 
C) a basic variable has a value of zero in the cj - zj row. 
D) a non-basic variable has a positive value in the cj - zj row.

Question 11

Which is not required for a problem to be in tableau form?

Accepted Answer

A) Each constraint must be written as an equation. 
B) Each of the original decision variables must have a coefficient of 1 in one equation and 0 in every other equation. 
C) There is exactly one basic variable in each constraint. 
D) The right-hand side of each constraint must be nonnegative. 
A) Each constraint must be written as an equation. 
B) Each of the original decision variables must have a coefficient of 1 in one equation and 0 in every other equation. 
C) There is exactly one basic variable in each constraint. 
D) The right-hand side of each constraint must be nonnegative.

Question 12

The purpose of the tableau form is to provide

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 13

A minimization problem with four decision variables, two greater-than-or-equal-to constraints, and one equality constraint will have

Accepted Answer

A) 2 surplus variables, 3 artificial variables, and 3 variables in the basis. 
B) 4 surplus variables, 2 artificial variables, and 4 variables in the basis. 
C) 3 surplus variables, 3 artificial variables, and 4 variables in the basis. 
D) 2 surplus variables, 2 artificial variables, and 3 variables in the basis. 
A) 2 surplus variables, 3 artificial variables, and 3 variables in the basis. 
B) 4 surplus variables, 2 artificial variables, and 4 variables in the basis. 
C) 3 surplus variables, 3 artificial variables, and 4 variables in the basis. 
D) 2 surplus variables, 2 artificial variables, and 3 variables in the basis.

Question 14

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

Accepted Answer

A) True 
 B)False

Question 15

Unit columns are used to identify

Accepted Answer

A) the tableau. 
B) the c row. 
C) the b column. 
D) the basic variables. 
A) the tableau. 
B) the c row. 
C) the b column. 
D) the basic variables.

Question 16

In the simplex method, a tableau is optimal only if all the cj - zj values are

Accepted Answer

A) zero or negative. 
B) zero. 
C) negative and nonzero. 
D) positive and nonzero. 
A) zero or negative. 
B) zero. 
C) negative and nonzero. 
D) positive and nonzero.

Question 17

To determine a basic solution set of n-m, the variables equal to zero and solve the m linear constraint equations for the remaining m variables.

Accepted Answer

A) True 
 B)False

Question 18

When there is a tie between two or more variables for removal from the simplex tableau,

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.

Question 19

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 20

The variable to remove from the current basis is the variable with the smallest positive cj - zj value.

Accepted Answer

A) True 
 B)False

Exam 17: LP: Simplex Method

We recognize infeasibility when one or more of the artificial variables do not remain in the solution at a positive value.

Infeasibility exists when one or more of the artificial variables

Which of the following is not a step that is necessary to prepare a linear programming problem for solution using the simplex method?

When a set of simultaneous equations has more variables than constraints,

The variable to enter into the basis is the variable with the largest positive cj - zj value.

A basic solution and a basic feasible solution

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

Every extreme point of the graph of a two variable linear programming problem is a basic feasible solution.

A basic feasible solution satisfies the nonnegativity restriction.

An alternative optimal solution is indicated when in the simplex tableau

Which is not required for a problem to be in tableau form?

The purpose of the tableau form is to provide

A minimization problem with four decision variables, two greater-than-or-equal-to constraints, and one equality constraint will have

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

Unit columns are used to identify

In the simplex method, a tableau is optimal only if all the cj - zj values are

To determine a basic solution set of n-m, the variables equal to zero and solve the m linear constraint equations for the remaining m variables.

When there is a tie between two or more variables for removal from the simplex tableau,

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.

The variable to remove from the current basis is the variable with the smallest positive cj - zj value.

Introduction

Introduction to Linear Programming

LP Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications

Advanced Linear Programming Applications

Distribution and Network Problems

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Forecasting

Markov Processes

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

The variable to enter into the basis is the variable with the largest positive c_j - z_j value.

In the simplex method, a tableau is optimal only if all the c_j - z_j values are

The variable to remove from the current basis is the variable with the smallest positive c_j - z_j value.