Blacktop Refining extracts minerals from ore mined at two different sites in Montana. Each ton of ore type 1 contains 20% copper, 20% zinc, and 15% magnesium. Each ton of ore type 2 contains 30% copper, 25% zinc, and 10% magnesium. Ore type 1 costs $90 per ton while ore type 2 costs $120 per ton. Blacktop would like to buy enough ore to extract at least 8 tons of copper, 6 tons of zinc, and 5 tons of magnesium in the least costly manner. Select the correct LP model for this problem.
Make sure that the equations for the objective function and each of the three constraints should be in the order of copper, zinc and magnesium respectively.
Let X1 represent Tons of ore purchased from mine 1.
Let X2 represent Tons of ore purchased from mine 2.
a. Formulate an LP model for this problem.
b. Sketch the feasible region for this problem.
c. Find the optimal solution.