This preview shows pages 1–3. Sign up to view the full content.
3.4.1
.
Factory
Process Cost
($/ton)
Reduction
Waste 1
Waste 2
1
15
0.1
0.45
2
10
0.2
0.25
3
20
0.4
0.3
Requirements:
reduce pollutant 1 by at least 30 tons
Reduce pollutant 3 by at least 40 tons
Variables:
For i = 1, 2, 3 let x
i
= Tons of processed Factory i waste.
Then appropriate LP is
min z =
15x
1
+ 10x
2
+ 20x
3
s.t.
.10x
1
+ .20x
2
+ .40x
3
≥
30(Pollutant 1)
.45x
1
+ .25x
2
+ .30x
3
≥
40(Pollutant 2)
x
1
≥
0,
x
2
≥
0,
x
3
≥
0
The following assumptions are reasonable because:
Proportionality:
 cost of processing from each factory contributes to the total cost linearly
 amount of pollutant reduced in each factory should contribute linearly to the total
pollutant reduction
i.e. no terms like
2
i
x
, where i = 1, 2, 3
Additivity:

cost of processing in each factory should be independent of each other

amount of pollution reduction in each factory should be independent of each
other
i.e. no terms like
12
x
x
∗
Divisibility:
 amount of waste can take on fractional values
Certainty :

we are given deterministic data.
No stochastic data
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document3.4.3
(a). Let x1 = units of food 1 bought and x2 = units of food 2 bought. Then we wish to solve
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '07
 Zhang

Click to edit the document details