A mining company produces 100 tons of red ore and 80 tons of black ore each week. These can be treated in different ways to produce three different alloys, Soft, Hard or Strong. To produce 1 ton of Soft alloy requires 5 tons of red ore and 3 tons of black. For the Hard alloy the requirements are 3 tons of red and 5 tons of black, whilst for the Strong alloy they are 5 tons of red and 5 tons of black. The profit per ton from selling the alloys (after allowing for production but not mining costs, which are regarded as fixed) are $250, $300 and $400 for Soft, Hard and Strong respectively. (a) Formulate the problem of deciding how much of each alloy to make each week (b) Solve the problem with Simplex Method (without using the simplex table and simplex calculator).
A mining company produces 100 tons of red ore and 80 tons of black ore each week. These can be treated in different ways to produce three different alloys, Soft, Hard or Strong. To produce 1 ton of Soft alloy requires 5 tons of red ore and 3 tons of black. For the Hard alloy the requirements are 3 tons of red and 5 tons of black, whilst for the Strong alloy they are 5 tons of red and 5 tons of black. The profit per ton from selling the alloys (after allowing for production but not mining costs, which are regarded as fixed) are $250, $300 and $400 for Soft, Hard and Strong respectively.
(a) Formulate the problem of deciding how much of each alloy to make each week
(b) Solve the problem with Simplex Method (without using the simplex table and simplex calculator).
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