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Engineering Optimization
ISYE3133C
Homework assignment # 2:
(due Monday February 18th at the beginning of the class, which means
electronic submission will be automatically closed at 10:05AM and you should hand in the handwritten
part at the beginning of the class)
•
Remember that you are allowed to work with others, just let me know who you worked with.
1.
a) Draw the feasible region of the following LP.
max
s
.
t
.
3
x
1
+
x
2
(1)
(2)
(3)
2
x
1
−
x
2
≤
2
−
x
1
−
5
x
2
≤ −
3
x
1
,
x
2
≥
0
b) Write the dual of the previous LP and draw the feasible region of the dual LP
c) Indicate if the original problem or its dual are infeasible or unbounded.
2.
Consider the following formulation for the heart valve problem (pg. 71 # 2):
Variables:
x
i
= amount of valves ordered from supplier
i
per month
min
z
=
5
x
1
+4
x
2
+3
x
3
s.t.
0
.
4
x
1
+0
.
3
x
2
+0
.
2
x
3
≥
500
(Buy enough large valves)
0
.
4
x
1
+0
.
35
x
2
+0
.
2
x
3
≥
300
(Buy enough medium valves)
0
.
2
x
1
+0
.
35
x
2
+0
.
6
x
3
≥
300
(Buy enough small valves)
x
1
≤
700
(Supplier limits)
x
2
≤
700
x
3
≤
700
x
1
, x
2
, x
3
≥
0
a) Write the dual of the heart valve problem formulated above. (Hint: remember that
is
equivalent to
b) The optimal (to the primal) is:
with z = $6450. Use this optimal
x
j
≤
700
−
x
j
≥ −
700
x
1
=
700,
x
2
=
700,
x
3
=
50,
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View Full Documentsolution to the primal and the rules of complementary slackness
to solve the dual problem. (Find the
optimal values of the dual variables and the objective function value.)
c)
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 Spring '08
 JuanPabloVielma
 Optimization

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