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.
|
Units of Nutrient per Pound of Feedstuff |
|||||
|
Nutrient |
Corn |
Wheat |
Barley |
Hay |
Minimum Daily Requirement |
|
Fat (gm) |
2 |
1 |
3 |
4 |
25 gm |
|
Protein (gm) |
20 |
15 |
15 |
10 |
400gm |
|
Iron (mg) |
4 |
7 |
6 |
5 |
125 mg |
|
Calories |
200 |
400 |
300 |
500 |
6,000 |
|
Cost per pound |
$0.60 |
$0.40 |
$0.35 |
$0.05 |
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.
