Answered: (2) Write the dual of the LP shown in…

Business

Operations Management

(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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Question

Please show all your work. Please answer all if you can.

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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