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 9 tons of copper, 7 tons of zinc, and 6 tons of magnesium in the least costly manner. (Let X₁ = tons of ore purchased from mine 1 and X₂ = tons of ore purchased from mine 2.)

(a) Formulate an LP model for this problem to minimize cost (in dollars).

MIN:

Subject to:

Copper (in tons):

Zinc (in tons):

Magnesium (in tons):

X₁, X₂ 0

(b) Sketch the feasible region.

c) What is the optimal solution?

(X₁, X₂) =