ORIE 320/520
PRELIM 2
Fall 2006
Tuesday November 7, 2006
7:30–9:00pm
90 minutes
1. (a)
[2 marks]
Deﬁne what we mean when we say a sequence of tableaux generated by
the simplex method is
cycling
.
(b)
[2 marks]
While the simplex method is cycling, can any of the basic feasible
solutions produced be nondegenerate? Justify your answer, based on your deﬁnition
in part (a).
(c)
[4 marks]
Solve the following linear program by the simplex method (
NOT
the
revised simplex method), using the smallest subscript rule for entering and leaving
variables. Begin with the basis [3
,
4
,
5]. State which basic feasible solutions you
encounter are degenerate, and which pivots you perform are degenerate.
maximize
x
1
+ 2
x
2
subject to
x
1

x
2
+
x
4
= 0
2
x
1

x
2
+
x
3
= 0
x
2
+
x
5
= 2
x
1
,
x
2
,
x
3
,
x
4
,
x
5
≥
0
.
1
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View Full Document2. Consider the following linear program.
maximize

2
x
1
+
x
2
subject to
x
1
+
x
2
+ 2
x
3
= 7
2
x
1
+
x
2
+ 3
x
3
= 10
x
1
,
x
2
,
x
3
≥
0
.
Consider the list of indices
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 Fall '08
 TODD
 Linear Programming, Optimization, Basic Feasible Solutions

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