Case Scenario: The Hoggs Corn and Wheat Farm
The Hogg company are a group of Oklahoma agricultural producers. The Hoggs want to derive a production process that will satisfy their goals. These farmers can produce corn, wheat, and/or hogs. The acreage they can cultivate for crops is 1100 acres, of which 600 acres is for corn production and 500 acres for wheat production. The Hogs have a maximum of 2000 hr of labor available for crop operations and 600 hr of labor for their hog operation. Corn production requires 1.6 hr of labor per acre, wheat requires 2.0 hr of labor per acre, and the hog operation requires 20 hr of labor per hog unit. This farm can produce 120 bushel of corn per acre and 32 bushel of wheat per acre. Corn and wheat can be sold on the market at $2.50 per bushel and $2.35 per bushel, respectively, and/or can be used as feed in the hog operation. Also, corn and wheat may be purchased from the city feed store at $2.70 per bushel and $2.55 pr bushel, respectively, for feeding the hogs. The hog unit requires 169.1 bushel of feed during a single production period. The corn and wheat used as hog feed can be transformed into corn equivalent units; that is, 1.1 bushel of wheat equals 1 bushel of corn.
The cost per acre to produce corn and wheat are $146.40 per acre and $48.60 per acre. The returns to the hog operation are $919.20 per hog unit. A hog unit is a sow and her litter, which are sold on the market. Returns to the hog operation are net values, for example, after maintenance and replacement stock cost.
The Hogg company is considering the following strategy:
Strategy 1:
As the goal with the highest priority, P1 they would like to see returns to the agriculture operation of at least $100,000. As their second priority, P2, at least three fourths of the land available for corn production and at least one-half of the land available for wheat production must be planted. The producers also desire that the under-planting of corn be weighed three times greater than that for wheat. The third and last priority goal P3, is that the hog operation be no greater than 40 hog units.
Formulate the problem in a goal programming format and solve for strategies 1 and 2. Discuss the results of whether the goals were achieved in each strategy and the corn, wheat and hog production output.