Problem:
The Longhorn Feeding Company (LFC) operates a feedlot to which cattle are brought for the final fattening process. Since LFC's cattle production averages 100,000, it is important to feed the cattle in a way that meets their nutritional requirements at a minimum cost.
The mixture LFC feeds the cattle is a blend of four feedstuffs: corn, wheat, barley, and hay. The table below provides the relevant dietary and cost information per pound of each feedstuff, as well as a cow's daily nutritional requirement. For example, for each pound of corn a cow consumes, it receives 2 grams of fat, 20 grams of protein, 4 milligrams of iron and 200 calories at a cost of $0.60.
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Units of Nutrient per Pound of Feedstuff
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Nutrient
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Corn
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Wheat
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Barley
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Hay
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Minimum Daily Requirement
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Fat (gm)
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2
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1
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3
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4
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25 gm
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Protein (gm)
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20
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15
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15
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10
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400gm
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Iron (mg)
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4
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7
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6
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5
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125 mg
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Calories
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200
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400
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300
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500
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6,000
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Cost per pound
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$0.60
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$0.40
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$0.35
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$0.05
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Required:
Question: Assuming a cow must consume exactly 24 pounds of feedstuff daily, write the linear programming formulation to determine the best feed mix for each cow daily.