Linear programming (LP): The linear programming (LP) is also known as linear optimization. Consider a mathematical model, and its requirements are used to represent by the linear relationships. The linear programming is the best method to achieve the best outcome of this mathematical model. The outcomes may be, maximum profit or lower cost. The linear optimization is also called as mathematical optimization because, it is a special case of mathematical programming. More formally, the LP is a technique for optimizing linear objective function subject to constraints of linear equality and linear inequality. Dual of LP: The dual of the given LP is another LP derived in the following schematic way from the original (the primal) LP. Every variable in the primal Linear Programming becomes a constraint in the dual LP. Every limit in the primal Linear Programming becomes a variable in the dual LP. In the dual LP, the objective direction is inversed. That is, the maximum in the primal becomes minimum in the dual and vice-versa.

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Answer 1

Question

Chapter 6.7, Problem 9P

Program Plan Intro

Linear programming (LP):

The linear programming (LP) is also known as linear optimization.

Consider a mathematical model, and its requirements are used to represent by the linear relationships. The linear programming is the best method to achieve the best outcome of this mathematical model. The outcomes may be, maximum profit or lower cost.

The linear optimization is also called as mathematical optimization because, it is a special case of mathematical programming.

More formally, the LP is a technique for optimizing linear objective function subject to constraints of linear equality and linear inequality.

Dual of LP:

The dual of the given LP is another LP derived in the following schematic way from the original (the primal) LP.

Every variable in the primal Linear Programming becomes a constraint in the dual LP.

Every limit in the primal Linear Programming becomes a variable in the dual LP.

In the dual LP, the objective direction is inversed. That is, the maximum in the primal becomes minimum in the dual and vice-versa.

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Answer 2

Question

Chapter 6.7, Problem 9P

Program Plan Intro

Linear programming (LP):

The linear programming (LP) is also known as linear optimization.

Consider a mathematical model, and its requirements are used to represent by the linear relationships. The linear programming is the best method to achieve the best outcome of this mathematical model. The outcomes may be, maximum profit or lower cost.

The linear optimization is also called as mathematical optimization because, it is a special case of mathematical programming.

More formally, the LP is a technique for optimizing linear objective function subject to constraints of linear equality and linear inequality.

Dual of LP:

The dual of the given LP is another LP derived in the following schematic way from the original (the primal) LP.

Every variable in the primal Linear Programming becomes a constraint in the dual LP.

Every limit in the primal Linear Programming becomes a variable in the dual LP.

In the dual LP, the objective direction is inversed. That is, the maximum in the primal becomes minimum in the dual and vice-versa.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 6.7, Problem 9P

Program Plan Intro

Linear programming (LP):

The linear programming (LP) is also known as linear optimization.

Consider a mathematical model, and its requirements are used to represent by the linear relationships. The linear programming is the best method to achieve the best outcome of this mathematical model. The outcomes may be, maximum profit or lower cost.

The linear optimization is also called as mathematical optimization because, it is a special case of mathematical programming.

More formally, the LP is a technique for optimizing linear objective function subject to constraints of linear equality and linear inequality.

Dual of LP:

The dual of the given LP is another LP derived in the following schematic way from the original (the primal) LP.

Every variable in the primal Linear Programming becomes a constraint in the dual LP.

Every limit in the primal Linear Programming becomes a variable in the dual LP.

In the dual LP, the objective direction is inversed. That is, the maximum in the primal becomes minimum in the dual and vice-versa.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 6.7, Problem 9P

Program Plan Intro

Linear programming (LP):

The linear programming (LP) is also known as linear optimization.

Consider a mathematical model, and its requirements are used to represent by the linear relationships. The linear programming is the best method to achieve the best outcome of this mathematical model. The outcomes may be, maximum profit or lower cost.

The linear optimization is also called as mathematical optimization because, it is a special case of mathematical programming.

More formally, the LP is a technique for optimizing linear objective function subject to constraints of linear equality and linear inequality.

Dual of LP:

The dual of the given LP is another LP derived in the following schematic way from the original (the primal) LP.

Every variable in the primal Linear Programming becomes a constraint in the dual LP.

Every limit in the primal Linear Programming becomes a variable in the dual LP.

In the dual LP, the objective direction is inversed. That is, the maximum in the primal becomes minimum in the dual and vice-versa.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 6.7, Problem 9P

Program Plan Intro

Linear programming (LP):

The linear programming (LP) is also known as linear optimization.

Consider a mathematical model, and its requirements are used to represent by the linear relationships. The linear programming is the best method to achieve the best outcome of this mathematical model. The outcomes may be, maximum profit or lower cost.

The linear optimization is also called as mathematical optimization because, it is a special case of mathematical programming.

More formally, the LP is a technique for optimizing linear objective function subject to constraints of linear equality and linear inequality.

Dual of LP:

The dual of the given LP is another LP derived in the following schematic way from the original (the primal) LP.

Every variable in the primal Linear Programming becomes a constraint in the dual LP.

Every limit in the primal Linear Programming becomes a variable in the dual LP.

In the dual LP, the objective direction is inversed. That is, the maximum in the primal becomes minimum in the dual and vice-versa.

Answer 6

Chapter 6.7, Problem 9P

Program Plan Intro

Linear programming (LP):

The linear programming (LP) is also known as linear optimization.

Consider a mathematical model, and its requirements are used to represent by the linear relationships. The linear programming is the best method to achieve the best outcome of this mathematical model. The outcomes may be, maximum profit or lower cost.

The linear optimization is also called as mathematical optimization because, it is a special case of mathematical programming.

More formally, the LP is a technique for optimizing linear objective function subject to constraints of linear equality and linear inequality.

Dual of LP:

The dual of the given LP is another LP derived in the following schematic way from the original (the primal) LP.

Every variable in the primal Linear Programming becomes a constraint in the dual LP.

Every limit in the primal Linear Programming becomes a variable in the dual LP.

In the dual LP, the objective direction is inversed. That is, the maximum in the primal becomes minimum in the dual and vice-versa.

Answer 7

Chapter 6.7, Problem 9P

Program Plan Intro

Linear programming (LP):

The linear programming (LP) is also known as linear optimization.

Consider a mathematical model, and its requirements are used to represent by the linear relationships. The linear programming is the best method to achieve the best outcome of this mathematical model. The outcomes may be, maximum profit or lower cost.

The linear optimization is also called as mathematical optimization because, it is a special case of mathematical programming.

More formally, the LP is a technique for optimizing linear objective function subject to constraints of linear equality and linear inequality.

Dual of LP:

The dual of the given LP is another LP derived in the following schematic way from the original (the primal) LP.

Every variable in the primal Linear Programming becomes a constraint in the dual LP.

Every limit in the primal Linear Programming becomes a variable in the dual LP.

In the dual LP, the objective direction is inversed. That is, the maximum in the primal becomes minimum in the dual and vice-versa.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 6.1 - Prob. 1P Ch. 6.1 - Prob. 2P Ch. 6.1 - Prob. 3P Ch. 6.1 - Prob. 4P Ch. 6.1 - Prob. 5P Ch. 6.2 - Prob. 1P Ch. 6.2 - Prob. 2P Ch. 6.3 - Prob. 1P Ch. 6.3 - Prob. 2P Ch. 6.3 - Prob. 3P

Solution Summary: The author explains that linear programming is a technique for optimizing linear objective function subject to constraints of linear equality and linear inequality.

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