3. 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 3 and Table 4 set the specifications of the problem: Table 3. Raw material characteristic Contents (%) Input item Aluminum Graphite Silicon Cost/ton ($) Available tons/day 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 4. Product Characteristic Ingot I Ingot II Ingredient Minimum Maximum Minimum Maximum Aluminum 8.1% 10.8% 6.2% 8.9% Graphite 1.5% 3.0% 4.1% 0 Silicon 2.5% 8 2.8% 4.1% Demand (tons/day) 130 Determine the optimal input mix the foundry should smelt. 250