# lect16 - Lecture 16 Linear Programming LP examples • A...

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Unformatted text preview: Lecture 16 Linear Programming 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. 60 3 2 ≤ + y x y x z 5 4 + = Feasible domain Optimal occurs at a vertex!!! . , 9 , 60 3 2 s.t. 5 4 max ≥ ≥ ≥ = + + + = w y x w y x y x z Slack Form . ) ( rank . s.t. max m A x b Ax cx z = ≥ = = What’s a vertex? . , ), ( 2 1 if vertex a called is polyhadren a in point A z y x z y z y x x = = Ω ∈ + = Ω ⇒ . of s in vertice found be can it then solution, optimal an has over max If . } | { Let Ω Ω ∈ ≥ Ω x cx Ax = b, x x = Fundamental Theorem . constraint one least at violates ' is, that , in not ' point a have must line the Thus, line. any contain not does However, solutions. optimal are *) ( line on points feasible all that follows It solutions. optimal also are and that means This . have must we 2, ) ( and , , * Since distinct. are , *, and 2 / ) ( * such that , exist there is, that not, is * suppose on, contraditi By . of vertex a is * that show will We solutions. optimal all among components zero of number maximum with * solution optimal an Consider x x y-x x*+ z y cz cx* = cy = / cy+cz cx* = cz cx* cy cx z y x z y x z y x x x Ω Ω ≥ ≥ + = Ω ∈ Ω α Proof. ion.ion....
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## This note was uploaded on 11/03/2010 for the course COMPUTER S CS 6363 taught by Professor Dingzhudu during the Fall '10 term at University of Texas at Dallas, Richardson.

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lect16 - Lecture 16 Linear Programming LP examples • A...

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