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IOE 310  Additional Problems B
For additional practice only. Not collected.
Problem 1
Consider the following LP:
max
z
=5
x
1
+3
x
2
+
x
3
s.t
2
x
1
+
x
2
+
x
3
≤
6
x
1
+2
x
2
+
x
3
≤
7
x
1
,
x
2
,
x
3
≥
0
(a) Graphically solve this problem.
(b) Use complementary slackness to solve the max problem.
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Page 2 of 9
Problem 2
Consider the following LP and its optimal tableau:
max
z
=5
x
1
+
x
2
+2
x
3
s.t
x
1
+
x
2
+
x
3
≤
6
6
x
1
++
x
3
≤
8
x
2
+
x
3
≤
2
x
1
,
x
2
,
x
3
≥
0
zx
1
x
2
x
3
s
1
s
2
s
3
rhs
1
0
1/6
0
0
5/6
7/6
9
0
0
1/6
0
1
1/6
5/6
3
0
1
1/6
0
0
1/6
1/6
1
00 1 1 0 0
1 2
(a) Find the dual to this LP and the optimal solution to the dual.
(b) Find the range of values of
c
2
for which the current basis remains optimal.
This additional problem set was developed for IOE 310, fall semester 2010. This document may not be copied or distributed.
IOE 310 – Additional Problems B
Page 3 of 9
Problem 3
Consider the following LP and its optimal tableau:
max
z
=3
x
1
+
x
2
−
x
3
s.t
2
x
1
+
x
2
+
x
3
≤
8
4
x
1
+
x
2
−
x
3
≤
10
x
1
,
x
2
,
x
3
≥
0
zx
1
x
2
x
3
s
1
s
2
rhs
1
0
0
1
1/2
1/2
9
00 1 3 2 
1 6
0
1
0
1
1/2
1/2
1
(a) Find the dual to this LP and the optimal solution to the dual.
(b) Find the range of values of
b
2
for which the current basis remains optimal. If
b
2
= 12, what is the
new optimal solution?
This additional problem set was developed for IOE 310, fall semester 2010. This document may not be copied or distributed.
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Page 4 of 9
Problem 4
Use the Theorem of Complementary Slackness to Fnd the optimal solution to the following LP and its dual:
max
z
=3
x
1
+4
x
2
+
x
3
+5
x
4
s.t
x
1
+2
x
2
+
x
3
x
4
≤
5
2
x
1
+3
x
2
+
x
3
x
4
≤
8
x
1
,
x
2
,
x
3
,
x
4
≥
0
Problem 5
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This note was uploaded on 12/20/2010 for the course IOE 310 taught by Professor Saigal during the Fall '08 term at University of Michigan.
 Fall '08
 Saigal

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