Aerial Products has received a contract to construct airframes produced at a client's factory in Tennessee. There are strict quality control measures in place for the airframes. The metal they are made of must meet the following content specifications:
|
Material
|
Minimum
|
Maximum
|
|
Manganese
|
5%
|
7%
|
|
Silicon
|
2%
|
3.4%
|
|
Carbon
|
.73%
|
1.29%
|
The metal consists of these materials as well as five other added products to make one airframe. The following table outlines the requirements for producing the metal for the airframe. Construct a linear program that optimizes cost while meeting the customers' requirements.
|
Material
|
Manganese
|
Silicon
|
Carbon
|
Pounds Available
|
Cost/lb.
|
|
AL1
|
20%
|
10%
|
1%
|
200
|
3$
|
|
AL 2
|
1%
|
.05%
|
3%
|
500
|
4$
|
|
Powder 1
|
15%
|
20%
|
.03%
|
1000
|
1500$
|
|
Powder 2
|
10%
|
12%
|
.05%
|
100
|
10000$
|
|
Ide 1
|
1%
|
2%
|
1%
|
50
|
.5$
|
|
Ide 2
|
5%
|
10%
|
5%
|
5
|
50000$
|
|
Metal 3
|
6%
|
4%
|
10%
|
15
|
12000$
|