Blacktop Refining extracts minerals from ore mined at two different sites in Montana. Each ton of ore type 1 contains 50% copper, 10% zinc, and 15% magnesium. Each ton of ore type 2 contains 15% 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.

a. Formulate an LP model for this problem.

b. Sketch the feasible region for this problem.

c. Find the optimal solution.