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.

Ore 1 = 28 tons

Ore 2 = 8 tons

Cost = $3480

Explanation:

Complete solution is provided in attached pictures. The Objective function line is dragged to the lowest edge of feasible region to obtain the optimum solution of (28,8).

That is 28 tons of Ore type-1 and 8 tons of Ore Type-2 should be ordered to incur minimum cost of $3480.

d

step-by-step explanation:

given

y + 3 = - 4(x - 2) ← distribute the parenthesis

y + 3 = - 4x + 8 ( subtract 3 from both sides )

y = - 4x + 5 → d

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4