A linear programming problem with the objective function 3x1 + 8x2 has the optimal solution x1 = 5,x2 = 6.If c2 decreases by 2 and the range of optimality shows 5 ≤ c2 ≤ 12,the value of Z

A) will decrease by 12. B) will decrease by 2. C) will not change. D) cannot be determined from this information. A) will decrease by 12. B) will decrease by 2. C) will not change. D) cannot be determined from this information.

Exam 18: Simplex-Based Sensitivity Analysis and Duality

Creative Kitchen Tools manufactures a wide line of gourmet cooking tools from stainless steel.For the coming production period,there is demand of 1200 for eight-quart stock pots and unlimited demand for three-quart mixing bowls and large slotted spoons.In the following model,the three variables measure the number of pots,bowls,and spoons to make.The objective function measures profit.Constraint 1 measures steel,constraint 2 measures manufacturing time,constraint 3 measures finishing time,and constraint 4 measures the stock pot demand. The final tableau is as follows: a.Calculate the range of optimality for c₁,c₂,and c₃. b.Calculate the range of feasibility for b₁,b₂,b₃,and b₄. c. Suppose that the inventory records were incorrect and the company really has only 14,000 units of steel.What effect will this have on your solution? d. Suppose that a cost increase will change the profit on the pots to $4.62.What effect will this have on your solution? e. Assume that the cost of time in production and finishing is relevant.Would you be willing to pay a $1.00 premium over the normal cost for 1000 more hours in the production department? What would this do to your solution?

(Essay)

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Question 21

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

(True/False)

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Question 22

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

(Multiple Choice)

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Question 23

We can often avoid the process of formulating and solving a modified linear programming problem by using the range of optimality to determine whether a change in an objective function coefficient is large enough to cause a change in the optimal solution.

(True/False)

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Question 24

Write the dual to the following problem.

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Question 25

A linear programming problem with the objective function 3x₁ + 8x₂ has the optimal solution x₁ = 5,x₂ = 6.If c₂ decreases by 2 and the range of optimality shows 5 ≤ c₂ ≤ 12,the value of Z

(Multiple Choice)

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Question 26

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 and b₂.

(Essay)

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Question 27

The range of optimality for a basic variable defines the objective function coefficient values for which that variable will remain part of the current optimal basic feasible solution.

(True/False)

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Question 28

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.

(True/False)

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Question 29

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

(True/False)

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Question 30

A dual price is associated with each decision variable.

(True/False)

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Question 31

Within the concept of duality is the original formulation of a linear programming problem known as the primal problem.

(True/False)

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Question 32

Showing 21 - 32 of 32

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

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

We can often avoid the process of formulating and solving a modified linear programming problem by using the range of optimality to determine whether a change in an objective function coefficient is large enough to cause a change in the optimal solution.

Write the dual to the following problem.

A linear programming problem with the objective function 3x₁ + 8x₂ has the optimal solution x₁ = 5,x₂ = 6.If c₂ decreases by 2 and the range of optimality shows 5 ≤ c₂ ≤ 12,the value of Z

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 and b₂.

The range of optimality for a basic variable defines the objective function coefficient values for which that variable will remain part of the current optimal basic feasible solution.

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

A dual price is associated with each decision variable.

Within the concept of duality is the original formulation of a linear programming problem known as the primal problem.

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

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

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

We can often avoid the process of formulating and solving a modified linear programming problem by using the range of optimality to determine whether a change in an objective function coefficient is large enough to cause a change in the optimal solution.

Write the dual to the following problem.

A linear programming problem with the objective function 3x1 + 8x2 has the optimal solution x1 = 5,x2 = 6.If c2 decreases by 2 and the range of optimality shows 5 ≤ c2 ≤ 12,the value of Z

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 and b2. ​

The range of optimality for a basic variable defines the objective function coefficient values for which that variable will remain part of the current optimal basic feasible solution.

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

A dual price is associated with each decision variable.

Within the concept of duality is the original formulation of a linear programming problem known as the primal problem.

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

A linear programming problem with the objective function 3x₁ + 8x₂ has the optimal solution x₁ = 5,x₂ = 6.If c₂ decreases by 2 and the range of optimality shows 5 ≤ c₂ ≤ 12,the value of Z

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 and b₂.