A steel factory that uses coal as its major source of energy causes three primary types of air pollution by releasing (1) particulate matter, (2) sulfur oxides, and (3) hydrocarbons. These three types of air pollution are caused by blast furnaces and open-hearth furnaces used in producing steel. The state has just passed a new clean air bill, which means that this factory must reduce its annual emission rate of particulates by 60 million pounds, sulfur oxides by 150 million pounds, and hydrocarbons by 125 million pounds. There are six pollution-abatement techniques (three for each type of furnace) that the factory can use to reduce air pollution. These six techniques, along with their per unit reduction for each pollutant, and their estimated annual cost per unit are listed below:
Taller Smokestacks Filters Better fuels
|
|
Blast
|
Open- Hearth
|
Blast
|
Open- Hearth
|
|
Blast
|
Open- Hearth
|
|
Pollutant
|
Furnace
|
Furnace
|
Furnace
|
Furnace
|
|
Furnace
|
Furnace
|
|
(per unit reduction in million pounds)
|
|
Particulate
|
12
|
9
|
25
|
20
|
|
17
|
13
|
|
Sulfur Oxides
|
35
|
42
|
18
|
31
|
|
56
|
49
|
|
Hydrocarbons
|
37
|
53
|
28
|
24
|
|
29
|
20
|
|
Cost/Unit
|
$80,000
|
$100,000
|
$70,000
|
$60,000
|
|
$110,000
|
$90,000
|
Assume that the factory's sole objective is to minimize the total cost of reducing emis- sions of these three pollutants to the new government standards by using any combina- tion of the six pollution abatement techniques. Set this up as an LP problem.