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1.
(25
points) Consider the following linear programming problem:
maxz=
3zi
+
2X2
+
5X3
+
X3
<
5
X2
+
x
3
ç
6
x1
+
x
2
+
x
3
<
15
xO
X2O
X3>O
(a)
(3
points) Write out this LP in standard form and explain why the Simplex Algorithm
starts with this
form.
3c+
2X
f
3
s
2
X2
=
/1
‘
7>
(b)
(5
points) Write out the matrix
A
and the vectors x,
b
and
c
so
that
the above standard
form can be
written
in
the matrix
form:
mazz=
cTx
Ax
=b
x>O
°
•
10
Oj
L’
c
2
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View Full DocumentIOE 310 Winter 2009
Midterm Exam
February 18, 2009
Name:
Instructions
•
This is a closed book, closed notes exam.
•
You may use one doublesided 8
×
11 inch note sheet and
no calculators
during the exam.
Note that not all problems carry the same weight. Do the problems that you are most com
fortable with ﬁrst and then move to others.
•
There are
3 problems
in the exam and
8 pages
(including this one). You can use the back
of each sheet for rough calculations.
•
Please write your solutions to each problem in the space provided. Show all work and write
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 Fall '09
 DennisBlumenfield

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