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:
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 75 2500 Aluminum briquette 100 0 0 900 Any amount Silicon briquette 0 0 100 380 Any amount 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 ∞
Silicon 2.5 ∞ 2.8 4.1 Demand (tons/day) 130 250 Develop an LP model to determine the optimal input mix the foundry should smelt, and find the solution using AMPL, Solver, or TORA.