The impact of adding an extra constraint to the feasible area of a solved linear programming problem. Introduction: Linear programming: It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution. Constraints: The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize an amount. Feasible region: A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

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Answer 1

Question

Chapter B, Problem 13DQ

a)

Summary Introduction

To determine: The impact of adding an extra constraint to the feasible area of a solved linear programming problem.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.

Constraints:

The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize an amount.

Feasible region:

A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

b)

Summary Introduction

To determine: The impact of adding an extra constraint to the optimal value of the objective function of a solved linear programming problem.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.

Constraints:

The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize a quantity.

Feasible region:

A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

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4. Consider the following linear programming problem: Maximize Z=$15x + $5y, subject to (1) 2x + y ≤ 10 and (2) 4x + 3y ≤ 24 and (3) x, y ≥ 0. Will the optimal solution change if the objective function becomes Maximize Z=$15x + $20y (constraints remain the same)? Select one: a. Can't determine given the information. b. Yes, it will change. c. No, it remains the same.

Consider the following set of constraints: 48Y >= 7296; 0.25 X + 12Y >= 1824, and X + Y <= 152. Pick a suitable statement for this problem: a. Solution to this problem cannot be found without the objective function. b. The feasible region is defined by a single (unique) point. c. It is a non-linear problem - unsuitable for grphical method. d. This problem has two feasible points - one is optimal for miniization problem and other is optimal for maximization problem. e. Feasible region is represented by a line and multiple feasible points are available.

A. What is the optimal solution and what is the optimal value of the objective function? B. Which constraints are binding? C. What are the dual values? Interpret each. D. If you could change the right-hand side of one constraint by one unit, which one would you choose? Why?

Answer 2

Question

Chapter B, Problem 13DQ

a)

Summary Introduction

To determine: The impact of adding an extra constraint to the feasible area of a solved linear programming problem.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.

Constraints:

The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize an amount.

Feasible region:

A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

b)

Summary Introduction

To determine: The impact of adding an extra constraint to the optimal value of the objective function of a solved linear programming problem.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.

Constraints:

The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize a quantity.

Feasible region:

A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

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Answer 3

Question

Chapter B, Problem 13DQ

a)

Summary Introduction

To determine: The impact of adding an extra constraint to the feasible area of a solved linear programming problem.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.

Constraints:

The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize an amount.

Feasible region:

A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

b)

Summary Introduction

To determine: The impact of adding an extra constraint to the optimal value of the objective function of a solved linear programming problem.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.

Constraints:

The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize a quantity.

Feasible region:

A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

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Answer 4

Question

Chapter B, Problem 13DQ

a)

Summary Introduction

To determine: The impact of adding an extra constraint to the feasible area of a solved linear programming problem.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.

Constraints:

The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize an amount.

Feasible region:

A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

b)

Summary Introduction

To determine: The impact of adding an extra constraint to the optimal value of the objective function of a solved linear programming problem.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.

Constraints:

The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize a quantity.

Feasible region:

A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

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Answer 5

Chapter B, Problem 13DQ

a)

Summary Introduction

To determine: The impact of adding an extra constraint to the feasible area of a solved linear programming problem.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.

Constraints:

The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize an amount.

Feasible region:

A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

b)

Summary Introduction

To determine: The impact of adding an extra constraint to the optimal value of the objective function of a solved linear programming problem.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.

Constraints:

The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize a quantity.

Feasible region:

A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

Answer 6

Chapter B, Problem 13DQ

a)

Summary Introduction

To determine: The impact of adding an extra constraint to the feasible area of a solved linear programming problem.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.

Constraints:

The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize an amount.

Feasible region:

A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

Answer 7

Chapter B, Problem 13DQ

a)

Summary Introduction

To determine: The impact of adding an extra constraint to the feasible area of a solved linear programming problem.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.

Constraints:

The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize an amount.

Feasible region:

A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

Answer 8

b)

Summary Introduction

To determine: The impact of adding an extra constraint to the optimal value of the objective function of a solved linear programming problem.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.

Constraints:

The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize a quantity.

Feasible region:

A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

Answer 9

b)

Summary Introduction

To determine: The impact of adding an extra constraint to the optimal value of the objective function of a solved linear programming problem.

Introduction:

Linear programming:

It is a linear optimization technique followed to develop the best outcome for the problem in hand. The outcome might be of maximum profit or less cost which is represented by a linear relationship. The outcome will take into consideration the constraints present in achieving the solution.

Constraints:

The constraints are the limitation for a situation within which the process must operate. The constraints are the limits within which the available resources can be utilized that will help to maximize or minimize a quantity.

Feasible region:

A feasible region is a solution space which contains all the possible points of an optimization problem. The region will be formed after satisfying the constraints in the problem which includes inequalities, integer constraints and inequalities. It is the area that is bounded by the constraints of the problem.

Answer 10

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Answer 11

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Answer 12

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Answer 13

Ch. B - Prob. 1DQ Ch. B - Prob. 2DQ Ch. B - Prob. 3DQ Ch. B - Prob. 4DQ Ch. B - Prob. 5DQ Ch. B - Prob. 6DQ Ch. B - Prob. 7DQ Ch. B - Prob. 8DQ Ch. B - Prob. 9DQ Ch. B - Prob. 10DQ

Solution Summary: The author explains the impact of adding an extra constraint to the feasible area of a solved linear programming problem.

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