max z c₁1 + €₂x2 + · = s.t. a111a12x2 + a21x1 + a22x2 + ai1x1 + a2x2+. tên n •+ainan C₁ + am2Ym > C2 + amjym > Cj ainy1 + a2ny2 +· Yi≥ 0, i = 1,...,m + amnym > Cn

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For the normal max problem, its dual is the normal min problem.

What is the complementary slackness? Please write the equations and then prove
them. 

max z = C₁x1 + €₂x2 + ·
a111a12*2 +
a21x1 + a22X2 +
s.t.
ai1x1 + a2x2 +
tenn
+ainan <b₁
+ a2nTn ≤ b₂
+ ainxn < bi
·+amnxn <bm
am 1x1am2x2 +
xj ≥ 0, j = 1,...,n
min w b1y1 + b2y2 +
=
s.t.
a11y1 + a2132 +
a12y1 + a22y2 +
...
a1jy1 + a2jy2 +
+bmym
+ amlym > C₁
+ am2Ym > C₂
• + AmjYm Z Cj
+ amnym z Cn
ainy1 + a2ny2 +
Yi20, i 1,...,m
Transcribed Image Text:max z = C₁x1 + €₂x2 + · a111a12*2 + a21x1 + a22X2 + s.t. ai1x1 + a2x2 + tenn +ainan <b₁ + a2nTn ≤ b₂ + ainxn < bi ·+amnxn <bm am 1x1am2x2 + xj ≥ 0, j = 1,...,n min w b1y1 + b2y2 + = s.t. a11y1 + a2132 + a12y1 + a22y2 + ... a1jy1 + a2jy2 + +bmym + amlym > C₁ + am2Ym > C₂ • + AmjYm Z Cj + amnym z Cn ainy1 + a2ny2 + Yi20, i 1,...,m
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