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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: Contents (%) Input item Cost/ton ($) Available tons/day Aluminum Graphite Silicon Steel scrap 10 5 4 100 1000 Aluminum scrap 95 1 2 150 500 Cast iron scrap 0 15 8 15 2500 Aluminum briquette 100 0 0 900 Any amount Silicon briquette 0 0 100 380 Any amount Table 1. Raw material characteristic Ingot Ingot 11 Ingredient Minimum Maximum Minimum Maximum Aluminum 8.1% 10.8% 6.2% 8.9% Graphite 1.5% 3.0% 4.1% oo Silicon 2.5% OO 2.8% 4.1% Demand (tons/day) 130 250 Table 2. Product Characteristic Determine the optimal input mix the foundry should smelt