Linear programming
A mining company produces 300 tons of red ore and 210 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 are $250, $300 and $400 for Soft, Hard and Strong, respectively. There is a weekly order of at least 15 tons for Soft alloy, and at least 15 tons for Hard alloy.
a) Let x = amount of Soft alloy (tons); y = amount of Hard alloy (tons); z = amount of Strong alloy (tons).
Set up the linear programming problem.
b) Find the optimal solution and optimal profit.
c) Which constraints are binding?
d) Understand all details on the Sensitivity report.
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