PLEASE SOLVE WITH EXCEL QM

8-16 (Material blending problem) Amalgamated Prod- ucts 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 con- trol standards for all of its component subcontrac- tors and has informed Amalgamated that each frame must have the following steel content: MINIMUM MAXIMUM MATERIAL PERCENTAGE PERCENTAGE Manganese 2.1 2.3 Silicon 4.3 4.6 Carbon 5.05 5.35 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 Amalgam- ated meets its requirements while minimizing costs. MANGANESE SILICON (%) CARBON (%) 15.0 30.0 MATERIAL AVAILABLE Alloy 1 Alloy 2 Alloy 3 Iron 1 Iron 2 Carbide 1 Carbide 2 Carbide 3 70.0 55.0 12.0 1.0 5.0 0 26.0 10.0 2.5 24.0 3.0 1.0 0 3.0 0 18.0 POUNDS COST PER AVAILABLE POUND ($) No limit 0.12 300 0.13 No limit 0.15 No limit 0.09 No limit 0.07 50 0.10 200 0.12 100 0.09 0 25.0 20.0 0 23.0 25.0