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Question 1 --- A foundry smelts steel, aluminum, and cast-iron scraps to produce two types of metal ingots, I and II, with specific limits on the aluminum, graphite and silicon contents. Aluminum and silicon briquettes may be used in the smelting process to meet the desired specifications. Table 1 and Table 2 set the specifications of the problem: Input item Contents (%) Aluminum Graphite Cost/ton ($) Available tons/day Silicon 10 5 4 100 1000 95 1 2 150 500 Steel scrap Aluminum scrap Cast iron scrap Aluminum briquette Silicon briquette 0 15 8 15 100 0 0 900 2500 Any amount Any amount 0 0 100 380 Table 1. Raw material characteristic Ingredient Ingot 1 Ingot 11 Minimum Maximum Minimum Maximum 8.1% 10.8% 6.2% 8.9% Aluminum Graphite 1.5% 3.0% 4.1% DO 2.8% 4.1% 250 Silicon 2.5% Demand (tons/day) 130 Table 2. Product Characteristic Determine the optimal input mix the foundry should smelt