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1
Dr. Maddah
ENMG 500 Engineering Management I
11/28/06
Duality (Continuous)
•
Economic Interpretation of duality
¾
A resource allocation example
.
Dakota furniture company
manufactures desks, tables and chairs.
The manufacturing of
each type of furniture requires three resources:
Lumber,
finishing labor, and carpentry labor.
The amount of each
resource needed to make one unit of a certain type of furniture
is as follows.
Desk
Table
Chair
Lumber
8 lft
6 lft
1 lft
Finishing hours
4 hrs
2 hrs
1.5 hrs
Carpentry hours
2 hrs
1.5 hrs
0.5 hrs
At present, 48 lft of lumber, 20 hours of finishing hours, and
eight hours of carpentry hours are available.
A desk sells for
$60, a table for $30, and a chair for $20.
How many of each
type of furniture should Dakota produce?
¾
Let
x
1
,
x
2
, and
x
3
respectively denote the number of desks,
tables and chairs produced.
Dakota problem is solved with
the following LP:
123
12
3
max
60
30
20
s.t.
8
6
48
4
2
1.5
20
2
1.5
0.5
8
0,
0,
0
xx
x
xxx
x
x
x
+
+
++≤
+
+≤
+
≥≥≥
¾
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 Fall '09
 DrBacelMaddah

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