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. The following tables set the specifications of the problem:

Develop an LP model to determine the optimal input mix the foundry should smelt, and find the solution using AMPL, Solver, or TORA.

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Input item Steel scrap Aluminum scrap Cast iron scrap Aluminum briquette Silicon briquette Contents (%) Aluminum Graphite 10 95 0 100 0 Ingredient Aluminum Graphite Silicon Demand (tons/day) 515 0 0 Silicon 4 2 Ingot I (%) Minimum 8.1 1.5 2.5 8 0 100 Maximum 10.8 3.0 ∞ 130 Cost/ton ($) 100 150 75 900 380 Ingot II (%) Minimum 6.2 4.1 2.8 Available (tons/day) 250 1000 500 2500 4.1 Any amount Any amount Maximum 8.9