If the dual price for b1 is 2.7,the range of feasibility is 20 ≤ b1 ≤ 50,and the original value of b1 was 30,which of the following is true?

A) There currently is no slack in the first constraint. B) We would be willing to pay up to $2.70 per unit for up to 20 more units of resource 1. C) If only 25 units of resource 1 were available,profit would drop by $13.50. D) All of these are correct. A) There currently is no slack in the first constraint. B) We would be willing to pay up to $2.70 per unit for up to 20 more units of resource 1. C) If only 25 units of resource 1 were available,profit would drop by $13.50. D) All of these are correct.

Exam 18: Simplex-Based Sensitivity Analysis and Duality

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.

Free

(True/False)

4.9/5

(31)

Question 1

Correct Answer:

Verified

True

For this optimal simplex tableau,the original right-hand sides were 100 and 90.The problem was a maximization. a.What would the new solution be if there had been 150 units available in the first constraint? b.What would the new solution be if there had been 70 units available in the second constraint?

Free

(Essay)

4.7/5

(27)

Question 2

Correct Answer:

Verified

The primal problem is as follows: The final tableau for its dual problem is as follows: Give the complete solution to the primal problem.

Free

(Essay)

4.9/5

(41)

Question 3

Correct Answer:

Verified

The complete primal solution is x₁ = 15,x₂ = 0,x₃ = 5,s₁ = 0,s₂ = 0,Z = 50.

For the following linear programming problem the final tableau is a.Find the range of optimality for c₁ and c₂. b.Find the range of feasibility for b₁,b₂,and b₃. c.Find the dual prices.

(Essay)

4.9/5

(28)

Question 4

As long as the actual value of the objective function coefficient is within the range of optimality,the current basic feasible solution will remain optimal.

(True/False)

4.8/5

(36)

Question 5

For the following linear programming problem the final tableau is a.Find the range of optimality for c_1, c_2, c_3, c_4, c_5, and c₆. b.Find the range of feasibility for b₁,b₂,and b₃.

(Essay)

4.7/5

(40)

Question 6

An LP maximization problem with all less-than-or-equal-to constraints and nonnegativity requirements for the decision variables is known as

(Multiple Choice)

4.9/5

(24)

Question 7

The range of optimality is calculated by considering changes in the c_j − z_j value of the variable in question.

(True/False)

4.7/5

(38)

Question 8

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

(True/False)

4.9/5

(39)

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?

(Essay)

4.7/5

(40)

Question 10

The dual variable represents the

(Multiple Choice)

4.8/5

(35)

Question 11

For the basic feasible solution to remain optimal,

(Multiple Choice)

4.7/5

(33)

Question 12

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

(True/False)

4.8/5

(35)

Question 13

Write the dual of the following problem:

(Essay)

4.8/5

(34)

Question 14

Dual prices and ranges for objective function coefficients and right-hand-side values are found by considering

(Multiple Choice)

4.8/5

(25)

Question 15

A one-sided range of optimality

(Multiple Choice)

4.9/5

(34)

Question 16

If the dual price for b₁ is 2.7,the range of feasibility is 20 ≤ b₁ ≤ 50,and the original value of b₁ was 30,which of the following is true?

(Multiple Choice)

4.9/5

(28)

Question 17

The improvement in the value of the optimal solution per unit increase in a constraint's right-hand side is

(Multiple Choice)

4.8/5

(31)

Question 18

The range of optimality is useful only for basic variables.

(True/False)

4.8/5

(40)

Question 19

Given the simplex tableau for the optimal primal solution,

(Multiple Choice)

4.9/5

(26)

Question 20

Showing 1 - 20 of 32

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.

The primal problem is as follows: The final tableau for its dual problem is as follows: Give the complete solution to the primal problem.

For the following linear programming problem the final tableau is a.Find the range of optimality for c₁ and c₂. b.Find the range of feasibility for b₁,b₂,and b₃. c.Find the dual prices.

As long as the actual value of the objective function coefficient is within the range of optimality,the current basic feasible solution will remain optimal.

For the following linear programming problem the final tableau is a.Find the range of optimality for c_1, c_2, c_3, c_4, c_5, and c₆. b.Find the range of feasibility for b₁,b₂,and b₃.

An LP maximization problem with all less-than-or-equal-to constraints and nonnegativity requirements for the decision variables is known as

The range of optimality is calculated by considering changes in the c_j − z_j value of the variable in question.

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

The dual variable represents the

For the basic feasible solution to remain optimal,

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

Write the dual of the following problem:

Dual prices and ranges for objective function coefficients and right-hand-side values are found by considering

A one-sided range of optimality

If the dual price for b₁ is 2.7,the range of feasibility is 20 ≤ b₁ ≤ 50,and the original value of b₁ was 30,which of the following is true?

The improvement in the value of the optimal solution per unit increase in a constraint's right-hand side is

The range of optimality is useful only for basic variables.

Given the simplex tableau for the optimal primal solution,

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

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

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.

The primal problem is as follows: ​ The final tableau for its dual problem is as follows: ​ Give the complete solution to the primal problem.

For the following linear programming problem ​ the final tableau is ​ a.Find the range of optimality for c1 and c2. b.Find the range of feasibility for b1,b2,and b3. c.Find the dual prices.

As long as the actual value of the objective function coefficient is within the range of optimality,the current basic feasible solution will remain optimal.

For the following linear programming problem ​ 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. ​

An LP maximization problem with all less-than-or-equal-to constraints and nonnegativity requirements for the decision variables is known as

The range of optimality is calculated by considering changes in the cj − zj value of the variable in question.

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

The dual variable represents the

For the basic feasible solution to remain optimal,

The entries in the associated slack column of the final tableau can also be interpreted as the changes in the values of the current basic variables corresponding to a one-unit increase in the right-hand side.​

Write the dual of the following problem: ​ ​

Dual prices and ranges for objective function coefficients and right-hand-side values are found by considering

A one-sided range of optimality

If the dual price for b1 is 2.7,the range of feasibility is 20 ≤ b1 ≤ 50,and the original value of b1 was 30,which of the following is true?

The improvement in the value of the optimal solution per unit increase in a constraint's right-hand side is

The range of optimality is useful only for basic variables.

Given the simplex tableau for the optimal primal solution,

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

Linear Programming: Simplex Method

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

The primal problem is as follows: The final tableau for its dual problem is as follows: Give the complete solution to the primal problem.

For the following linear programming problem the final tableau is a.Find the range of optimality for c₁ and c₂. b.Find the range of feasibility for b₁,b₂,and b₃. c.Find the dual prices.

For the following linear programming problem the final tableau is a.Find the range of optimality for c_1, c_2, c_3, c_4, c_5, and c₆. b.Find the range of feasibility for b₁,b₂,and b₃.

The range of optimality is calculated by considering changes in the c_j − z_j value of the variable in question.

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

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

Write the dual of the following problem:

If the dual price for b₁ is 2.7,the range of feasibility is 20 ≤ b₁ ≤ 50,and the original value of b₁ was 30,which of the following is true?