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Unformatted text preview: Homework 3
Some help for difficult problems The dual of nonstandard
forms If Xi≥0, then the dual has the "proper"
≥0,
form for the ith restriction.
form If that dual is a max, then the ith
If
restriction will be ≤.
restriction If that dual is a min, then the ith
If
restriction will be ≥. The dual of nonstandard
forms If Xi≤0, then the dual has the "wrong"
≤0,
form for the ith restriction.
form If that dual is a max, then the ith
If
restriction will be ≥.
restriction If that dual is a min, then the ith
If
restriction will be ≤. Duals of nonstandard forms
Duals If Xi is unrestricted, then constraint i in
If
the dual will be an equality.
the McCarl and Spreen have a chart you can
McCarl
refer to when developing duals for nonrefer
standard forms.
standard Conversion to standard form An inequality going the "wrong way" is
An
multiplied through by 1 and "flipped" to
the correct way. An equality becomes two constraints,
An
one a LE the other a GE. Then, the one
that is the "wrong way" is multiplied
through by 1 and "flipped" to the correct
way. Conversion to standard form If Xi≤0, replace with Xineg and multiply
≤0,
every coefficient in the column by 1.
every If Xi unrestricted, use Xipos and Xineg.
If
Xipos will have same coffecients as Xi.
Xineg will have the coefficients multiplied
by 1. Multiple uses for products
Multiple Each possible use for a product must
Each
have its very own column.
have You can't share the column with other
You
products being converted to the same
item or you will be counting the use
multiple times.
multiple Example I can produce corn or sugar cane and sell
can
the raw product. Or I can use the corn or sugar cane to
Or
produce a syrup. Sample solutions follow. Syrup problem
production constraint
transfer yield corn
transfer yield sugar can
syrup transfer corn
syrup transfer  cane
total syrup
syrup limit
answers Produce
Corn
(acres)
$90.00
1
95 Produce
Cane
(acres)
$80.00
1 Sell
Corn
(bu)
$3.00 Sell
Cane
(tons)
$30.00 Corn for Cane for make
make
total
Syrup
Syrup syrup corn syrup cane syrup
(bu)
(tons) (gallons) (gallons) (gallons)
$10.00 1
35 1
1 1
3 1
8
1 10.53 189.47 0.00 6631.58 1000.00 Note the large number of activities. 0.00 1
1 3000.00 0.00 1
1
3000.00 RHS
LE
LE
LE
LE
LE
EQ
LE 200
0
0
0
0
0
3000 212842.11
200.00
0.00
0.00
0.00
0.00
0.00
3000.00 meat problem You need separate variables for grinding
You
different cuts into hamburger (3
variables).
variables). If you don't use separate variables, the
If
model overcounts the amount of product
needed to make hamburger. Incorrect Specification
Meat Variety Hamb Chuck Round Steak Loin Rib Misc
0.6
0.85 0.5 0.75 1.2 0.8 1.2 0.2
chuckt 0.29
1
1
roundt 0.22
1
1
steakt 0.19
1
loint
0.16
1
1
ribt
0.09
1
misct
0.05
1
hlimit
1
meatlim 1
var trans
1
answers 569
27
0
165 125.2 108.1 91.04 51.21 28.45
rc
0
0
0
0
0
0
0
0
0 le 0
le 0
le 0
le 0
le 0
le 0
le 50
le 569
le 27 limits SP
462.3
0.0 0.5
0.0 0.8
0.0 1.2
0.0 0.8
0.0 1.2
0.0 0.2
0.0 0.3
569.0 0.8
27.0 0.6 Juice Problem
How many activities do you need?
Production – 3 activities (3 varieties)
Sales of fruit – 2 activities (2 varieties can be
Sales
sold as fruit)
sold Putting aside fruit for juice (3 activities, one for
Putting
each variety of fruit)
each Using the setaside fruit for a kind of juice (6
Using
activities, 2 types of juice times 3 sets of
activities for putting fruit aside for juice)
activities Selling juice (2 activities)
Selling Juice Problem – part a
Juice Restrictions (rows)
amount of land to produce oranges
market limit for fresh Rich Fibers
3 transfer rows to take produced fruit and distribute to
transfer
fresh market or the setaside for juice
fresh
3 transfer rows to move setaside fruit to juice A and/or
transfer
Juice B production.
Juice
Two "blending" restrictions for A and B (volume)
Two quality restrictions for juice A
Two quality restrictions for juice B.
Two
final obj value = $118,028.99 ...
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 Fall '08
 Duffy,P

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