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Lecture 10/30/02
Use of Simplex Tableaus
•
Unbounded LP’s
•
LP’s with Equality or
≥
Constraints
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View Full Document Steps in Solving LP’s (Revised)
1. Put problem in standard form
2. Find an intial bfs.
3. Determine if optimal.
4. If not determine entering BV
a. If max LP, choose NBV having coefficient <0 in Row 0.
b. If min LP, choose NBV having coefficient >0
in Row 0.
5. Use ratio test to determine which BV becomes NBV.
6. Use ERO’s to find next bfs.
7. Go to step 3.
LP’s with Unbounded Solution
Problem #3 on P.158
Although x
1
can enter basis LP is unbounded. Why?
Given following tableau while solving a max LP:
z
x
1
x
2
x
3
x
4
RHS
1
3
2
0
0
0
0
1
1
1
0
8
0
2
0
0
1
5
Answer: Bring x
2
into basis.
column are nonpositive, minimum ratio rule can’t
be applied. x
2
and z can increase without bound.
Since all entries in pivot
=> z=3 x
1
+ 2 x
2
= 2 x
2
=> x
3
= 8+ x
2
 x
1
= 8+ x
2
= > x
4
=5  2 x
1
=5
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View Full Document LP’s with Unbounded Solution
An unbounded LP for a max (min) problem occurs
when a NBV with a negative (positive) coefficient
in Row 0 has nonpositive coefficients in each
constraint.
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This note was uploaded on 04/17/2008 for the course CSA 273 taught by Professor Patton during the Spring '08 term at Miami University.
 Spring '08
 Patton

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