Finding Feasible Solutions To A Linear Programming Worksheet - Columbia University In The City Of New York Page 12

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An infeasible LP
Let’s see what happens if our original LP is infeasible. Consider the LP:
maximize
x
(54)
1
subject to
x
+ x
7
(55)
1
2
x
+ x
6
(56)
1
2
x
, x
0 .
(57)
1
2
We add slack variable s
to the first inequality, excess and artificial vari-
1
able to the second, and obtain:
z =
x
M a
(58)
1
1
a
= 7
x
x
+ e
(59)
1
1
2
1
s
= 6
x
x
(60)
1
1
2

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