Question 1

​Explain why the zj value for a slack variable is the dual price.

Accepted Answer

In linear programming, the zj value for

Question 2

The range of feasibility indicates right-hand side values for which

Accepted Answer

A)  the value of the objective function will not change. 
B)  the values of the decision variables will not change. 
C)  those variables which are in the basis will not change. 
D)  more simplex iterations must be performed. 
A)  the value of the objective function will not change. 
B)  the values of the decision variables will not change. 
C)  those variables which are in the basis will not change. 
D)  more simplex iterations must be performed.

Question 3

​When sensitivity calculations yield several potential upper bounds and several lower bounds, how is the range
determined?

Accepted Answer

When sensitivity calculations yield seve

Question 4

​For an objective function coefficient change outside the range of optimality, explain how to calculate the new optimal
solution. Must you return to the (revised) initial tableau?

Accepted Answer

When dealing with linear programming pro

Question 5

The entries in the associated slack column of the final tableau indicate the changes in the values of the current basic variables corresponding to a one-unit increase in the right-hand side.

Accepted Answer

A) True 
 B)False

Question 6

The dual price for an equality constraint is the zj value for its artificial variable.

Accepted Answer

A) True 
 B)False

Question 7

For the following linear programming problem
Max Z
−2x1 + x2 − x3
s.t.
2x1 + x2 ≤ 7
1x1 + x2 + x3 ≥ 4
​
the final tableau is   ​ 
a.Find the range of optimality for c1, c2 , c3. c4, c5 , and c6.
b.Find the range of feasibility for b1, and b2.

Accepted Answer

a.c₁ ≤ 2 0 ≤ c₂ c₃ ≤ 0

Question 8

The dual price is the improvement in value of the optimal solution per unit increase in the value of the right-hand side associated with a linear programming problem.

Accepted Answer

A) True 
 B)False

Question 9

For this optimal simplex tableau, the right-hand sides for the two original ≥ constraints were 300 and 250. The problem was a minimization.   ​ 
a.
What would the new solution be if the right-hand side value in the first constraint had been 325?
b.
What would the new solution be if the right-hand side value for the second constraint had been 220?

Accepted Answer

a.x₃ = 50, x₁ = 75,

Question 10

The ranges for which the right-hand side values are valid are the same as the ranges over which the dual prices are valid.

Accepted Answer

A) True 
 B)False

Question 11

​Explain the simplex tableau location of the dual constraint for each type of constraint.

Accepted Answer

In the simplex tableau, the dual constra

Question 12

Given the following linear programming problem
Max Z
0.5x1 + 6x2 + 5x3
s.t.
4x1 + 6x2 + 3x3 ≤ 24
1x1 + 1.5x2 + 3x3 ≤ 12
3x1 + x2 ≤ 12
​
and the final tableau is   ​ 
a.Find the range of optimality for c1, c2, c3, c4, c5, and c6.
b.Find the range of feasibility for b1, b2, and b3.

Accepted Answer

a.c₁ ≤ 4 2.5 < c₂ ≤ 10

Question 13

If the simplex tableau is from a maximization converted from a minimization, the signs and directions of the inequalities that give the objective function ranges will need to be adjusted to apply to the original coefficients.

Accepted Answer

A) True 
 B)False

Question 14

As long as the objective function coefficient remains within the range of optimality, the variable values will not change although the value of the objective function could.

Accepted Answer

A) True 
 B)False

Question 15

The dual variable represents

Accepted Answer

A)  the marginal value of the constraint 
B)  the right-hand side value of the constraint 
C)  the artificial variable 
D)  the technical coefficient of the constraint 
A)  the marginal value of the constraint 
B)  the right-hand side value of the constraint 
C)  the artificial variable 
D)  the technical coefficient of the constraint

Explain why the zj value for a slack variable is the dual price.

The range of feasibility indicates right-hand side values for which

When sensitivity calculations yield several potential upper bounds and several lower bounds, how is the range determined?

For an objective function coefficient change outside the range of optimality, explain how to calculate the new optimal solution. Must you return to the (revised) initial tableau?

The entries in the associated slack column of the final tableau indicate the changes in the values of the current basic variables corresponding to a one-unit increase in the right-hand side.

The dual price for an equality constraint is the z_j value for its artificial variable.

For the following linear programming problem Max Z −2x₁ + x₂ − x₃ s.t. 2x₁ + x₂ ≤ 7 1x₁ + x₂ + x₃ ≥ 4 the final tableau is a.Find the range of optimality for c₁, c₂ , c₃. c₄, c₅ , and c₆. b.Find the range of feasibility for b₁, and b₂.

The dual price is the improvement in value of the optimal solution per unit increase in the value of the right-hand side associated with a linear programming problem.

The ranges for which the right-hand side values are valid are the same as the ranges over which the dual prices are valid.

Explain the simplex tableau location of the dual constraint for each type of constraint.

If the simplex tableau is from a maximization converted from a minimization, the signs and directions of the inequalities that give the objective function ranges will need to be adjusted to apply to the original coefficients.

As long as the objective function coefficient remains within the range of optimality, the variable values will not change although the value of the objective function could.

The dual variable represents

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

Linear Programming: Simplex Method

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

Exam 18: Simplex-Based Sensitivity Analysis and Duality

​Explain why the zj value for a slack variable is the dual price.

The range of feasibility indicates right-hand side values for which

​When sensitivity calculations yield several potential upper bounds and several lower bounds, how is the range determined?

​For an objective function coefficient change outside the range of optimality, explain how to calculate the new optimal solution. Must you return to the (revised) initial tableau?

The entries in the associated slack column of the final tableau indicate the changes in the values of the current basic variables corresponding to a one-unit increase in the right-hand side.

The dual price for an equality constraint is the zj value for its artificial variable.

For the following linear programming problem Max Z −2x1 + x2 − x3 s.t. 2x1 + x2 ≤ 7 1x1 + x2 + x3 ≥ 4 ​ the final tableau is ​ a.Find the range of optimality for c1, c2 , c3. c4, c5 , and c6. b.Find the range of feasibility for b1, and b2.

The dual price is the improvement in value of the optimal solution per unit increase in the value of the right-hand side associated with a linear programming problem.

The ranges for which the right-hand side values are valid are the same as the ranges over which the dual prices are valid.

​Explain the simplex tableau location of the dual constraint for each type of constraint.

Given the following linear programming problem Max Z 0.5x1 + 6x2 + 5x3 s.t. 4x1 + 6x2 + 3x3 ≤ 24 1x1 + 1.5x2 + 3x3 ≤ 12 3x1 + x2 ≤ 12 ​ and the final tableau is ​ a.Find the range of optimality for c1, c2, c3, c4, c5, and c6. b.Find the range of feasibility for b1, b2, and b3.

If the simplex tableau is from a maximization converted from a minimization, the signs and directions of the inequalities that give the objective function ranges will need to be adjusted to apply to the original coefficients.

As long as the objective function coefficient remains within the range of optimality, the variable values will not change although the value of the objective function could.

The dual variable represents

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

Linear Programming: Simplex Method

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

Explain why the zj value for a slack variable is the dual price.

When sensitivity calculations yield several potential upper bounds and several lower bounds, how is the range determined?

For an objective function coefficient change outside the range of optimality, explain how to calculate the new optimal solution. Must you return to the (revised) initial tableau?

The dual price for an equality constraint is the z_j value for its artificial variable.

For the following linear programming problem Max Z −2x₁ + x₂ − x₃ s.t. 2x₁ + x₂ ≤ 7 1x₁ + x₂ + x₃ ≥ 4 the final tableau is a.Find the range of optimality for c₁, c₂ , c₃. c₄, c₅ , and c₆. b.Find the range of feasibility for b₁, and b₂.

Explain the simplex tableau location of the dual constraint for each type of constraint.