Lecture 9B

Lecture 9B - Desk Problem: An LP Paradigm max c t x Ax = b...

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EE103 Lec 9B (SEJ) 1 Desk Problem: An LP Paradigm D 1 D 2 D 3 D 4 Carpentry shop 49 7 1 0 Finishing shop 11 3 4 0 6,000 labor hours 4,000 labor hours D 1 D 2 D 3 D 4 Profit 12 20 18 40 1234 123 4 12 3 4 max12 20 18 40 .. 4 9 7 10 6000 3 4000 0, 1,. ..,4 i xxxx st x x x x xx x x xi +++ +++≤ ++ + ≥= max 0 t cx A xb x = EE103 Lec 9B (SEJ) 2 zx x x x =+++ max 0 0 0 0 34 4 9 7 10 0 3 40 3 4 12 20 18 40 0 ..,6 z xx x xz x x z z i + + + + +≤ = We’ll put this LP problem in a form that’s Suitable to implement the Simplex Algorithm Desk Problem: An LP Paradigm
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EE103 Lec 9B (SEJ) 3 max 4 9 7 10 0 6000 5 123 4 3 40 4000 12 3 4 6 z xx x x x z x x x z +++ + += ++ + = 20 18 0 0 0 5 1234 6 0, 1,. ..,6 xxxxx x z xi i + + +− = ≥= We’ll convert the first two equality constraints to equality constraints by the addition of two new “slack” variables. Desk Problem: An LP Paradigm /1000, ..,4,5,6 j jj ←= EE103 Lec 9B (SEJ) 4 max 4 9 7 6 5 3 4 ( ) 3 4 6 0 z xxx x x z x x x z T + + = 0 0 0 12345 6 ..,6 x z i + = Desk Problem: An LP Paradigm
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EE103 Lec 9B (SEJ) 5 Desk Problem: An LP Paradigm () 567 123 03 3 1 3 [,,][, 6 ,] 0, 0, 0, 0, 4 ,, 0 x t x B aaa eee I BIx == = 547 1 1 1 [,, ] ?0 , 0 0, 0, , , 0 .1 5 , 4 t Ba a a Bx =
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This note was uploaded on 03/30/2009 for the course EE 103 taught by Professor Vandenberghe,lieven during the Winter '08 term at UCLA.

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Lecture 9B - Desk Problem: An LP Paradigm max c t x Ax = b...

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