CO350 L
INEAR
O
PTIMIZATION
 HW 9
Due Date:
Friday July 13th, at 2pm, in the drop box outside the Tutorial Center.
Recall, late assignments will not be graded.
Exercise 1.
Consider the following linear program (P)
max
{
c
T
x
:
Ax
=
b, x
≥
0
}
where
A
=
"
1
1
2
0
2
2
3
3
1
2
#
b
=
"
3
7
#
c
=
5
8
4
2
3
(1) Formulate the auxiliary problem (P’).
(2) Solve (P’) using the
revised
simplex.
(3) Solve (P) using the
revised
simplex starting from the solution obtained for (P’).
Exercise 2.
Let
B
:=
{
x
∈ <
n
:
x
T
x
≤
1
}
. Recall,
k
x
k
=
√
x
T
x
corresponds to the length of
x
. Thus
B
is the set of points in an
n
dimensional space which are at distance at most
1
from the origin, i.e.
B
is the
n
dimensional unit sphere. It is intuitively clear that a sphere is convex. In this exercise, you are asked to
give an algebraic proof (using the definition of convexity seen in class) of the fact that
B
is convex.
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 Spring '07
 S.Furino,B.Guenin
 Simplex algorithm, Polytope, following linear program, unit sphere

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