Note: It should be solve manually with complete solution. Use of excel is not allowed.

Material Blending Problem 1. 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: MINIMUM PERCENTAGE MAXIMUM PERCENTAGE MATERIAL Manganese Silicon 2.1 2.3 4.3 4.6 Carbon 5.05 5.35 Amalgamated mixes batches of eight different available materials to produce one ton of steel used in the body frames. The table below details these materials. MANGANESE (%) SILICON (%) 15.0 CARBON (%) POUNDS AVAILABLE COST PER POUND ($) 70.0 3.0 No limit 0.12 MATERIAL AVAILABLE Alloy 1 Alloy 2 Alloy 3 Iron 1 Iron 2 55.0 30.0 1.0 300 26.0 0 12.0 1.0 10.0 3.0 No limit No limit No limit 0.13 0.15 0.09 0.07 0.10 5.0 2.5 0 0 24.0 18.0 50 Carbide 1 Carbide 2 0 25.0 20.0 200 0.12 Carbide 3 0 23.0 25.0 100 0.09 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 minimizing costs. 2. Refer to Problem No 1. Find the cause of the difficulty and recommend how to adjust it. Then solve the problem again