February 11, 2006`
QUIZ 2
1.
Write the dual of the following LP problem
Maximize z = 5x1 + 6x2
Subject to
x1 + 2x2 = 5
-x1 + 5x2 3
x1 is unrestricted and x2 0
2.
The primal solution of an LP maximization problem is as follows.
Cb BV
2 x2
5 x3
0 s3
Z
zj
1350 cj-zj
cj
3
Xb x1
100 -0.25
230 1.50
20 2
7
-4
2
x2
1
0
0
2
0
5
x3
0
1
0
5
0
0
0
0
s1 s2 s3
0.5 -0.25 0
0 0.5 0
-2
1
1
1
2
0
-1 -2
0
The primal problem is as follows
Maximise z = 3x1 + 2 x2 + 5x3
Subject to
x1 + 2x2 + x3 < 430
3x1 + 2x3 < 460
x1 + 4x2 < 420 and all x1, x2 & x3 > 0
The management has increased all resources by 30 %. Find out whether the
solution still holds good. Give p
roper explanation.