Question 1

A basic feasible solution satisfies the nonnegativity restriction.

Accepted Answer

A) True 
 B)False

Question 2

​What is the criterion for entering a new variable into the basis?

Accepted Answer

In the context of linear programming, pa

Question 3

​A manager for a food company is putting together a buffet and she is trying to determine the best mix of
​
crab and steak to be served. Below are variable definitions she developed including vitamin, mineral and protein requirements. Also included below is an optimal simplex tableau she obtained from her
computations. She is interested in interpreting what it means.
​
Variable definitions:
xl = amount of crab (oz) to be served per buffet batch
x2 = amount of steak (oz) to be served per buffet batch
s1 = vitamin A units provided in excess of requirements
s2 = mineral units provided in excess of requirements
s3 = protein units provided in excess of requirements
Optimal tableau   ​

Accepted Answer

​
Optimal solution: 15 ounces of crab in

Question 4

​The operations research analyst for a big manufacturing firm in Oregon developed the following variable definitions for a 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 5

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 6

Comment on the solution shown in this simplex tableau.

Accepted Answer

The tableau indicate

Question 7

What coefficient is assigned to an artificial variable in the objective function?

Accepted Answer

A)  zero. 
B)  one. 
C)  a very large negative number. 
D)  a very large positive number. 
A)  zero. 
B)  one. 
C)  a very large negative number. 
D)  a very large positive number.

Question 8

The values in the cj − zj , or net evaluation, row indicate

Accepted Answer

A)  the value of the objective function. 
B)  the decrease in value of the objective function that will result if one unit of the variable corresponding to the jth column of the A matrix is brought into the basis. 
C)  the net change in the value of the objective function that will result if one unit of the variable corresponding to the jth column of the A matrix is brought into the basis. 
D)  the values of the decision variables. 
A)  the value of the objective function. 
B)  the decrease in value of the objective function that will result if one unit of the variable corresponding to the jth column of the A matrix is brought into the basis. 
C)  the net change in the value of the objective function that will result if one unit of the variable corresponding to the jth column of the A matrix is brought into the basis. 
D)  the values of the decision variables.

Question 9

​Describe and illustrate graphically the special cases that can occur in a linear programming solution. What clues for these cases does the simplex procedure supply?

Accepted Answer

In linear programming, there are several

Question 10

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

Accepted Answer

A) True 
 B)False

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

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 13

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 14

Write the following problem in tableau form. Which variables would be in the initial basis?
Max
x1 + 2x2
s.t.
3x1 + 4x2 ≤ 100
2x1 + 3.5x2 ≥ 60
2x1 − 1x2 = 4
x1 , x2 ≥ 0

Accepted Answer

Max x₁ + 2x₂ − Ma₁ − Ma₂ s.t. 3x

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

Solve the following problem by the simplex method.
Max
100x1 + 120x2 + 85x3
s.t.
3x1 + 1x2 + 6x3 ≤ 120
5x1 + 8x2 + 2x3 ≤ 160
x1 , x2 , x3 ≥ 0

Accepted Answer

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

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 19

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.

Question 20

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

Accepted Answer

A) True 
 B)False

A basic feasible solution satisfies the nonnegativity restriction.

What is the criterion for entering a new variable into the basis?

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

Comment on the solution shown in this simplex tableau.

What coefficient is assigned to an artificial variable in the objective function?

The values in the c_j − z_j , or net evaluation, row indicate

Describe and illustrate graphically the special cases that can occur in a linear programming solution. What clues for these cases does the simplex procedure supply?

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

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

An alternative optimal solution is indicated when in the simplex tableau

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

Write the following problem in tableau form. Which variables would be in the initial basis? Max x₁ + 2x₂ s.t. 3x₁ + 4x₂ ≤ 100 2x₁ + 3.5x₂ ≥ 60 2x₁ − 1x₂ = 4 x₁ , x₂ ≥ 0

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

Solve the following problem by the simplex method. Max 100x₁ + 120x₂ + 85x₃ s.t. 3x₁ + 1x₂ + 6x₃ ≤ 120 5x₁ + 8x₂ + 2x₃ ≤ 160 x₁ , x₂ , x₃ ≥ 0

The variable to enter into the basis is the variable with the largest positive c_j − z_j 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 system of simultaneous equations has more variables than equations, there is a unique solution.

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

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

A basic feasible solution satisfies the nonnegativity restriction.

​What is the criterion for entering a new variable into the basis?

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

Comment on the solution shown in this simplex tableau.

What coefficient is assigned to an artificial variable in the objective function?

The values in the cj − zj , or net evaluation, row indicate

​Describe and illustrate graphically the special cases that can occur in a linear programming solution. What clues for these cases does the simplex procedure supply?

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

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

An alternative optimal solution is indicated when in the simplex tableau

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

Write the following problem in tableau form. Which variables would be in the initial basis? Max x1 + 2x2 s.t. 3x1 + 4x2 ≤ 100 2x1 + 3.5x2 ≥ 60 2x1 − 1x2 = 4 x1 , x2 ≥ 0

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

Solve the following problem by the simplex method. Max 100x1 + 120x2 + 85x3 s.t. 3x1 + 1x2 + 6x3 ≤ 120 5x1 + 8x2 + 2x3 ≤ 160 x1 , x2 , x3 ≥ 0

The variable to enter into the basis is the variable with the largest positive cj − zj 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 system of simultaneous equations has more variables than equations, there is a unique solution.

Introduction

An Introduction to Linear Programming

Linear Programming: Sensitivity Analysis and Interpretation of Solution

Linear Programming Applications in Marketing, Finance, and Operations Management

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

What is the criterion for entering a new variable into the basis?

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

The values in the c_j − z_j , or net evaluation, row indicate

Describe and illustrate graphically the special cases that can occur in a linear programming solution. What clues for these cases does the simplex procedure supply?

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

Write the following problem in tableau form. Which variables would be in the initial basis? Max x₁ + 2x₂ s.t. 3x₁ + 4x₂ ≤ 100 2x₁ + 3.5x₂ ≥ 60 2x₁ − 1x₂ = 4 x₁ , x₂ ≥ 0

Solve the following problem by the simplex method. Max 100x₁ + 120x₂ + 85x₃ s.t. 3x₁ + 1x₂ + 6x₃ ≤ 120 5x₁ + 8x₂ + 2x₃ ≤ 160 x₁ , x₂ , x₃ ≥ 0

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