March 2014
Intermediate to advanced
412 pages
11h 16m
English
Content preview from Numerical Methods and Optimization
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Duality and Sensitivity Analysis in Linear Programming 291
This LP is, clearly, infeasible. The dual of this LP is
minimize 2y
1
− 3y
2
subject to 2y
1
− 2y
2
≥ 5
−y
1
+ y
2
≥−2
x
1
,x
2
≥ 0,
whichisalsoinfeasible.
The correspondence between the primal and dual LP types is summarized
below.
Primal LP
Dual LP
Optimal Infeasible Unbounded
Optimal possible impossible impossible
Infeasible impossible possible possible
Unbounded impossible possible impossible
12.5 Complementary Slackness
In this section, we explore the relationship between the constraints of the
primal LP and the variables of its dual when both problems are optimal. Let
theprimalLPbegivenby
maximize
n
j=1
c
j
x
j
sub
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