(Material blending problem) Amalgamated Products has just received a contract to construct steel body frames for automobiles that are to be produced at a new Japanese auto 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 1 ton of steel for use in the body frames. The table on this page details these materials.
Formulate and solve the LP problem, indicating how much of each of the eight materials should be blended into a 1-ton load of steel so that Amalgamated meets its requirements while minimizing costs.

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MATERIAL MINIMUM PERCENTAGE MAXIMUM PERCENTAGE Manganese 2.1 2.3 Silicon 4.3 4.6 Carbon 5.05 5.35