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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
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.
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