STOR 415 Handout
Sensitivity analysis: an example
Consider the problem
max
z
= 41
x
1
+25
x
2
s.t.
3
x
1
+2
x
2
+
x
3
= 10
5
x
1
+3
x
2
+
x
4
= 16
x
1
,
···
, x
4
≥
0
.
The initial tableau (called tableau 1):
z
x
1
x
2
x
3
x
4
rhs
Basic var
1
41
25
0
0
0
z
= 0
0
3
2
1
0
10
x
3
= 10
0
5
3
0
1
16
x
4
= 16
After several iterations, we arrive at the tableau below (called tableau 2),
which shows the optimal BFS in which
x
1
and
x
2
are basic variables:
z
x
1
x
2
x
3
x
4
rhs
Basic var
1
0
0
2
7
132
z
= 132
0
1
0
3
2
2
x
1
= 2
0
0
1
5
3
2
x
2
= 2
Change the objective eﬃcient for
x
3
Note that
x
3
is a nonbasic variable in tableau 2. Let us consider changing
its eﬃcient in the objective function from 0 to
δ
.
The initial tableau (note that it is not a valid simplex tableau, because
x
3
is a basic variable in this tableau, and its coeﬃcient in row 0 needs to be
0):
z
x
1
x
2
x
3
x
4
rhs
Basic var
1
41
25

δ
0
0
z
= 0
0
3
2
1
0
10
x
3
= 10
0
5
3
0
1
16
x
4
= 16
After conducting the same EROs that bring tableau 1 to tableau 2, we
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 Spring '11
 ShuLu
 Operations Research, Linear Programming, Optimization, Simplex algorithm, δ, Basic var

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