Problem 8 Two alloys, A and B, are made from four metals, I, II, III, and IV, according to the follow- ing specifications: Alloy Selling price ($) 200 Specifications At most 80% of I At most 30% of II At least 50% of IV Between 40% and 60% of II At least 30% of III At most 70% of IV B 300 The four metals are extracted from three ores according to the following data: Constituents (%) Ore 1 2 3 Maximum quantity (tons) 1000 2000 3000 1 20 10 30 10 20 30 5 5 70 IV 30 30 20 Others 10 10 0 Price/ton ($) 30 40 50 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. (Hint: Let Xkj be tons of ore i allocated to alloy k, and define wk as tons of alloy k produced.)