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Chapter 7 Linear Programming I. Simplex Method Ding-Zhu Du

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LP examples A post office requires different numbers of full- time employees on different days of the week. The number of full-time employees required on each day is given in the table. Union rules state that each full-time employee must work five consecutive days and then receive two days off. The post office wants to meet its daily requirements using only full-time employees. Formulate an LP that the post office can use to minimize the number of full-time employees that must be hired.

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Feasible domain Optimal occurs at a vertex!!!

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Slack Form

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Whats a vertex?

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Fundamental Theorem

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Proof.

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Proof (conts).

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Characterization of Vertex

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Proof

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Basic Feasible Solution

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Optimality Condition

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Sufficiency

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Nondegeneracy Assumption Remark

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Necessary

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(pivoting)

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Simplex Method

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Simplex Table

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Puzzle 1

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Artificial Feasible Basis

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Puzzle 2

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lexicographical ordering

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Method

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Method(cont)

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Theorem

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Puzzle 3

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Complexity of LP

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Thanks, End

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Duality for linear programming. Illustration of the notion Consider an enterprise producing r items: f k = demand for the item k =1,…, r using s components:

Duality for linear programming. Illustration of the notion Consider an enterprise producing r items: f k = demand for the item k =1,…, r using s components:

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