A farmer has the following resource endowments: 1,000 acres of land, 1,500 hours of family labor, and $30,000 of capital investment. She can use these resources to grow the following crops: corn, sorghum, wheat, and soybeans. The farmer expects the fol- lowing in terms of crop yields, prices, variable costs, and labor requirements.
|
Crop
|
Price ($/bushel)
|
Yield (bushel/acre)
|
Variable Cost ($/acre)
|
Labor Requirement (hours/acre)
|
|
Corn
|
2.75
|
120
|
250
|
3.25
|
|
Sorghum
|
2.65
|
100
|
200
|
3.00
|
|
Wheat
|
3.15
|
105
|
245
|
3.15
|
|
Soybeans
|
6.75
|
45
|
230
|
3.30
|
Also, the farmer can invest any part of her $30,000 to rent additional land at $100 per acre and hire additional labor at $6 per hour.
Assume that the farmer works to maximize net revenue (gross revenue minus vari- able costs) from the production of these four crops. Formulate this as an LP.