ORIE 3300/5300
ASSIGNMENT 8
Fall 2010
*NOT TO BE TURNED IN**
Solutions will be posted 5 pm, Saturday November 6.
1. Consider the linear programming problem
max
2
x
1
+
3
x
2
+
2
x
3
3
x
1
+
2
x
2
+
x
3
≤
7
2
x
1
+
x
2
+
x
3
≤
4
x
1
,
x
2
,
x
3
≥
0
.
Add slack variables and solve this problem by the revised simplex
method, starting with the allslack basis. Use the most positive re
duced cost rule to choose the entering index.
2. This question is concerned with the linear programming problem in
Q2 of Assignment 7.
(a) Write out the dual of this problem.
(b) Use your answer for Q2 last week to ﬁnd the optimal solution of
the dual problem you found in (a).
(c) Give a short certiﬁcate that the solution you found in (b) is indeed
the optimal solution of the dual problem.
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 '08
 TODD
 Linear Programming, Optimization, optimal solution, linear programming problem

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