CO350 LINEAR OPTIMIZATION
Due Date:
Friday January 26th at the beginning of class. Please do NOT leave the assignments in the drop
off box but return them to the instructor in class.
From the notes:
•
exercise 3.3.1
•
exercise 3.3.2
•
exercise 3.3.3
Exercise 1.
Consider the following linear program (P):
max
c
T
x
s.t.
Ax
=
b
Fx
≤
d
Note, the variables
x
are free.
(1) Rewrite (P) so that it is in standard equality form. Compute then the dual (D) of the LP you obtain
using the formula for problems in standard equality form.
(2) Give a self contained proof that (D) is indeed the dual of (P) along the same line as the proof of
Theorem 4.1.
Exercise 2.
You are given numbers
a
1
,a
2
,...,a
k
. Recall (see assignment 1) that the following LP (P) ﬁnds
the maximum value among numbers
a
1
,a
2
,...,a
k
.
min
y
s.t.
y
≥
a
i
(
i
= 1
,...,k
)
(1) Write the dual (D) of the LP (P) given above.
(2) Find an optimal solution for (D).
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 Winter '07
 S.Furino,B.Guenin
 Operations Research, Optimization, Dual problem, standard equality form

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