OEM DMOR Homework #4
Fall 2007
For all problems:
Please show your work; credit is given for the method used (not just
for having the correct final answer).
I have no problem with you using software to check
your answers.
Question 1 (15 points).
Use the simplex method to find the optimal solution to the
following problem.
Add slacks to the formulation to put it in standard form, and use
those slacks as your initial basic variables.
Max
3
x
1
+
x
2
+
x
3
s.t.
x
1
+
x
2
≤ 6
x
2
+
x
3
≤ 12
x
1
+
x
2
+ 2
x
3
≤ 20
All
x
≥ 0.
Question 2 (15 points).
Use the simplex method to find the optimal solution to the
following problem.
Use
x
1
and
x
3
as your initial basic variables.
(This means you need to
do a little GaussJordan work before you can begin the simplex method.)
Min
x
1
– 3
x
2
+
x
3
–
x
4
s.t.
x
1
–
x
2
+
x
3
+ 2
x
4
= 15
–2
x
1
+
x
2
+
x
3
–
x
4
= 0
All
x
≥ 0.
Questions 3 through 9 (5 points each).
Now, the remaining questions are related to
sensitivity analysis.
Consider the following example.
I am trying to figure out how to fill up my cooler for this weekend’s tailgating party.
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 Fall '09
 VLADIMIRLBOGINSKI
 Optimization, Gatorade, optimal solution, initial basic variables

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