# linear programming

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Exeter Mines produces iron ore at four different mines; however, the ores extracted at each mine are different in their iron content. Mine 1 produces magnetite ore, which has a 70% iron content; mine 2 produces limonite ore, which has a 60% iron content; mine 3 produces pyrite ore, which has a 50% iron content; and mine 4 produces taconite ore, which has only a 30% iron content. Exeter has three customers that produce steel Armco, Best, and Corcom. Armco needs 400 tons of pure (100%) iron, Best requires 250 tons of pure iron, and Corcom requires 290 tons. It costs $37 to extract and process 1 ton of magnetite ore at mine 1,$46 to produce 1 ton of limonite ore at mine 2, $50 per ton of pyrite ore at mine 3, and$42 per ton of taconite ore at mine 4. Exeter can extract 350 tons of ore at mine 1; 530 tons at mine 2; 610 tons at mine 3; and 490 tons at mine 4. The company wants to know how much ore to produce at each mine in order to minimize cost and meet its customers' demand for pure (100%) iron.
a. Formulate a linear programming model for this problem.
b. Do any of the mines have slack capacity? If yes, which one(s)?
c. If Exeter Mines could increase production capacity at any one of its mines, which should it be? Why?
d. If Exeter were to decide to increase capacity at the mine identified in (b), how much could it increase capacity before the optimal solution point (i.e., the optimal set of variables) would change?
6. ### linear programming

Exeter Mines produces iron ore at four different mines; however, the ores extracted at each mine are different in their iron content. Mine 1 produces magnetite ore, which has a 70% iron content; mine 2 produces limonite ore, which …
7. ### Chimestry

(Iron ore is impure Fe_2O_3. When Fe_2O_3 is heated with an excess of carbon (coke), metallic iron and carbon monoxide gas are produced. From a sample of ore weighing 950kg , 533kg of pure iron is obtained). What is the mass percent …
8. ### Chemistry

Iron ores have different amounts of iron per kilogram of ore. Calculate the mass percent composition of iron for each iron ore: Fe2O3{\rm Fe_2O_3} (hematite), Fe3O4{\rm Fe_3O_4} (magnetite), FeCO3{\rm FeCO_3} (siderite).
9. ### Chemistry

1.630 g of iron ore is dissolved in an acidic solution. This solution is titrated to a pink endpoint with 27.15 mL of a 0.020 M KMnO4 solution. a. How many moles of MnO4- ions were consumed?
10. ### Chemistry

A 0.446-gram sample of iron ore is dissolved in HCl and the iron (Fe solid) is reduced to Fe2+. The solution is then titrated by 38.6mL of 0.105 N KMn)4. Calculate the percentage of Fe in the iron ore sample.

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