U. of Illinois MATH 482 Lecture 5 In class exercises
•
The goal of this worksheet is to supplement the material in
Lecture 5 that introduces the simplex method.
•
I hope this will help guide you through some of the Fner points
of that lecture.
•
Please feel free to ask questions at any time.
1. Solve the following LP:
minimize
z
=

6
x
1
+ 8
x
3
subject to

3
x
1
+ 3
x
2
+ 2
x
3
+
x
4
= 7
2
x
1

x
3
+
x
5
= 1
2
x
1
+
x
2

3
x
3
+
x
6
= 0
(a) Write down the tableau (using the obvious basis).
(b) What is the basic feasible solution? What is the objective value
at this basic feasible solution?
(c) There is a column
j
with
c
j
<
0. What variable
x
j
is that
associated to?
1
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(Q1 continued)
(d) The ratio test says that in this column we look for the smallest
positve
b
r
/a
rj
and use column
r
to pivot. To explain this rule, note
that if we make
x
j
a little bigger than 0, the objective value drops.
How big can we make
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 Spring '08
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 Math, Optimization, basic feasible solution

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