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Questions and Answers
What is the primary purpose of deriving the dual from the primal in linear programming?
What is the primary purpose of deriving the dual from the primal in linear programming?
When converting a greater than or equal to (≥) type inequality in a maximization problem, which of the following steps should be taken?
When converting a greater than or equal to (≥) type inequality in a maximization problem, which of the following steps should be taken?
What should be done to an equal to (=) type constraint for a minimization problem?
What should be done to an equal to (=) type constraint for a minimization problem?
In the context of linear programming, how should an unrestricted-in-sign decision variable be treated?
In the context of linear programming, how should an unrestricted-in-sign decision variable be treated?
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Which statement is true regarding the conversion of inequalities for a minimization problem?
Which statement is true regarding the conversion of inequalities for a minimization problem?
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Study Notes
Duality in Linear Programming
- Linear programming models have two forms: primal and dual.
- The primal is the original form of the model.
- The dual is an alternative model derived from the primal.
- The dual provides an alternative perspective on the problem.
Steps for Converting a Primal Problem to a Dual Problem (Non-Normal LP Problem)
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Step 1: Convert the non-normal LP problem to normal form.
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Maximization Problems:
- Inequalities:
- '≤' type: No change required.
- '≥' type: Multiply by -1; change to '≤'.
- '=' type: Convert to two inequalities, one '≤' and one '≥'.
- Unrestricted-in-sign variables: Rewrite as the difference of two non-negative variables.
- Inequalities:
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Minimization Problems:
- Inequalities:
- '≤' type: Multiply by -1; change to '≥'.
- '≥' type: No change required.
- '=' type: Convert to two inequalities, one '≥' and one '≤'.
- Unrestricted-in-sign variables: Rewrite as the difference of two non-negative variables.
- Inequalities:
-
Maximization Problems:
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Description
Explore the concepts of primal and dual forms in linear programming. Learn the steps to convert a non-normal LP problem to its dual form, including maximization and minimization scenarios. This quiz will enhance your understanding of alternative perspectives in linear problem-solving.
