Reference no: EM132244428

Two Oklahoma agricultural producers, Ima Hogg and Ura Hogg, 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 is for wheat production. The Hoggs have a maximum of 2000 hours of labor available for crop operations and 600 hours of labor for their hog operation. Corn production requires 1.6 hours of labor per acre, wheat requires 2.0 hours of labor per acre, and the hog operation requires 20 hours of labor per hog unit. This farm can produce 120 bu of corn per acre and 32 bu 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 per bushel, respectively, for feeding the hogs. The hog unit requires 169.1 bu. of feed during a single production period. The corn and wheat used as hog feed can be transformed in corn equivalent units; that is 1.1 bu of wheat equals 1 bu of corn.

The costs per acre to produce corn and wheat were $146.40 per acre and $46.60 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 costs.

Ima and Ura Hogg are considering two strategies.

Strategy 1:

As the goal with the highest priority, they would like to see returns to the agricultural operation of at least $100,000. As their second priority, 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 weighted three times greater than that for wheat. The third and last priority is that the hog operation be no greater than 40 hog units.

Strategy 2:

The Hoggs have been concerned for some time with the steady decrease in grain market prices, and they are seriously considering joining a regional agricultural movement that favors limiting current production. Their highest priority will continue to be a return of at least $100,000. For their second priority, a hog operation of 40 units or more is desired. Remaining resources are to be allocated to plant no more than three-fourths of their corn land and no more than one-half of their wheat land, as a third priority.

Develop solutions for both strategies.