IOE 310  Problem Set 06
Solution
Suggested Reading
Section 4.14 (p.184186) (skip Example 9)
Section 6.1
Section 6.2 (ignore (10”)’ for artiFcial variables on p.272)
Problem 1
Section 4.14 Problem 4 (p.189)
Professor Kaufman Comments:
I disagree with the solution for Problem 1, which I post below. I am interested in seeing your
solutions. If you have a solution, please give it. If you agree with the solution’s manual, please
give the same solution but with added justiFcation. The part I don’t understand is: why can
a B±S not have both z’ and z” be positive? Justify this. Otherwise, if you disagree with the
solutions manual, please justify why you disagree  a counterexample perhaps.
You will receive full credit too if you just copy the answer below. However, I would rather
you think.
The solution from the textbook is:
max
z
=
z
°
+
z
°°
s.t
4
x
1
+
x
2
≤
4
2
x
1
−
x
2
≤
0
.
5
2
x
1
−
3
x
2
=
z
°
−
z
°°
All variables nonnegative
±irst note that in any basic feasible solution,
z
°
and
z
°°
cannot both be positive. Then observe that if
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 Fall '08
 Saigal
 Operations Research, Optimization, $ 23, $ 26, $ 21.50

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