Amalgamated Products has just received a contract to construct steel body frames for automobiles that are to be produced at the new Japanese factory in Tennessee. The Japanese auto manufacturer has strict quality control standards for all of its component subcontractors and has informed Amalgamated that each frame must have the following steel content:

Amalgamated mixes batches of eight different available materials to produce one ton of steel used in the body frames. The table on this page details these materials.

Formulate and solve the LP model that will indicate how much each of the eight materials should be blended into a 1-ton load of steel so that Amalgamated meets its requirements while minimizingcosts.

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MINIMUM MAXIMUM MATERIAL Manganese Silicon Carbon PERCENTAGEPERCENTAGE 2.1 4.3 5.05 2.3 4.6 5.35 MATERIAL AVAILABLE Alloy 1 Alloy 2 Alloy 3 Iron 1 Iron 2 Carbide 1 Carbide 2 Carbide 3 MANGANESE SILICON CARBON COST PER POUND (S) 0.12 0.13 0.15 0.09 0.07 0.10 0.12 0.09 AVAILABLE 70.0 55.0 12.0 15.0 30.0 26.0 10.0 2.5 24.0 25.0 23.0 3.0 No limit 300 No limit No limit No limit 50 200 100 0 0 0 0 18.0 20.0 25.0