Chapter 7 Linear Programming

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Chapter 7Linear 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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Optimal occurs at a vertex!!!
Feasible domain
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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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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