(2) Write the dual of the LP shown in part (1). (3) List at least two reasons why linear programming duality is useful.
(2) Write the dual of the LP shown in part (1). (3) List at least two reasons why linear programming duality is useful.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Transcribed Image Text:2.
Short answers
(1) Construct the phase-I LP for the following linear program (don't solve it!):
max z = a1 - 12
s.t. r2 + x3 < 1
- T1 + a3 24
*i + x2 - x3 = 2
a1 free , r2 2 0, rs 2 0.
(2) Write the dual of the LP shown in part (1).
(3) List at least two reasons why linear programming duality is useful.
Page 4
(4) Consider the following simplex tableau for a maximization problem:
Row z
1
X4 I5 rhs
8
0 0
a
-1
2
0 -60 20 0
3
d
5
e
The entries a, b, c, d, e are unknown parameters. Find conditions on these entries so
that the linear program is unbounded.
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