A steel company is producing steel for a new contract. The contract specifies the information in the following table for the steel. MATERIAL MINIMUM MAXIMUM Maganese 2.10% 3.10% Silicon 4.30% 6.30% Carbon 1.05% 2.05% The steel company mixes batches of eight different available materials to produce each ton of 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 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.% 18.0% 50 $0.10 Carbide 2 0% 25.0% 20.0% 200 $0.12 Carbide 3 0% 23.% 25.0% 100 $0.09