Two alloys, A and B, are made from four metals, I, II, III, and IV, according to the following specifications:

The four metals are extracted from three ores according to the following data:

Develop an LP model to determine how much of each type of alloy should be produced, and find the solution using AMPL, Solver, or TORA. Let x_ij be tons of ore i allocated to alloy j, and define W_j as tons of alloy j produced.

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Alloy A B Specifications At most 80% of I At most 30% of II At least 50% of IV Between 40% and 60% of II At least 30% of III At most 70% of IV Selling price ($) 200 300