This preview shows pages 1–2. Sign up to view the full content.
MthSc810 – Mathematical Programming
Fall 2011, Homework #8. Due Thursday, October 27, 2011, 6PM EDT.
From the syllabus: homework will be penalized
50%
for each day they are late.
After two days, they will not be accepted.
No exception.
Problem 1.
Write the dual of the following problems:
1. The KleeMinty example for general
n
;
2. The bank loan model seen in lecture 2, slide 21;
3. The production planning model (same lecture, slide 11).
Problem 2.
Consider the following problem:
min 6
x
1
+ 4
x
2
s.t. x
1
+
x
2
= 1
3
x
1
+
x
2
≥
0
x
1
≤
0
x
2
≥
0
.
1. Write its dual;
2. Solve the dual with the graphical method;
3. Find an optimal solution of the primal by applying complementary slackness.
4. Verify the primal’s optimal solution by solving the primal through the graph
ical method.
Problem 3.
Solve the following problem, after writing its standard form, by
means of the dual simplex method. Use the initial basis
B
=
{
3
,
4
}
. Note that
the initial basis is only dual feasible.
min
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '08
 Staff
 Math

Click to edit the document details