A steel company is producing steel for a new contract. The contract specifies the information in the followingtable for the steel. According to the specification. The table at the bottom of this page details these materials. Formulate and solve the LP model that will indicate how much of each of the eight materials should be blended into a 1-ton load of steel so that the company can meet the specifications under the contract while minimizing costs.

MATERIAL

MINIMUM MAXIMUM

Manganese 2.10% 3.10%

Silicon 4.30% 6.30%

Carbon 1.05% 2.05%

Table for Problem 3-34

MATERIAL AVAILABLE MANGANESE SILICON CARBON POUNDS AVAILABLE COST PER POUND

Alloy 1 70.0% 15.0% 3.0% No limit $0.12

Alloy 2 55.0% 30.0% 1.0% 300 $ 0.13

Alloy 3 12.0% 26.0% 0% No limit $0.15

Iron 1 1.0% 10.0% 3.0% No limit $0.09

Iron 2 5.0% 2.5% 0% No limit $0.07

Carbide 1 0% 24.0% 18.0% 50 $0.10

Carbide 2 0% 25.0% 20.0% 200 $0.12

Carbide 3 0% 23.0% 25.0% 100 $0.09