This preview shows pages 1–2. Sign up to view the full content.
Recitation 9 Problems
More Practice Problems for Midterm II
These problems are intended to aid in your understanding of the topics.
Please make sure
you also understand everything from the practice midterm.
15.053 Introduction to Optimization
April 19,2002
1.
Consider the following linear program.
M
a
xz=4
x
1
+x
2
+2
x
3
s.t.
x
2
x
3
<=
4
x
1
+3
x
3
<= 1
2x
1
3
x
2
<= 2
x
1
,x
2
3
>= 0
a)
Formulate the dual of the above linear program
b)
Use duality to show that the optimal objective function value of the primal problem is 0.
(Hint: Find a feasible point.)
2.
Consider the following network flow problem, where the arcs are defined with (u
ij
, c
ij
), and
the lower bounds are 0:
Find the optimal flows using the network simplex method.
Use the following spanning tree
(the dashed line indicates nonbasic flow at its upper bound.
All other nonbasic flows are at
the lower bound):
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document3.
The US Olympic Team is trying to put together a relay team for the 400meter relay.
Each
swimmer must swim 100 meters of breaststroke, backstroke, butterfly or freestyle.
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '05
 Prof.JamesOrlin

Click to edit the document details