A farmer owns 500 acres of land, which are suitable for growing corn, soybeans, and sunflowers. His expectations are that the net profit from producing each crop is: $55 per acre for corn, $60 per acre for soybeans, and $50 per acre for sunflowers. He and his family can supply 3,000 hours per year in performing all the farm operations necessary to grow these crops. In addition, he is endowed with the equivalent of 4,500 hours of tractor time necessary to grow these crops. Assume that the only resources necessary in crop production are land, labor, and tractor time. The technol- ogy is summarized below.
|
Resource (Unit)
|
Corn
|
Crop
Soybeans
|
Sunflowers
|
Resource Endowment
|
|
Land (acres)
|
1.0
|
1.0
|
1.0
|
500
|
|
Labor (hours)
|
0.4
|
0.2
|
0.3
|
3,000
|
|
Tractor (hours)
|
0.5
|
0.2
|
0.4
|
4,500
|
Assuming that the farmer's objective is to maximize total profits, what is the LP model for this problem? Solve this problem using the simplex method.