4. (10pt) A farmer is deciding how much corn, soybeans, and wheat to plant in the...

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4. (10pt) A farmer is deciding how much corn, soybeans, and wheat to plant in the coming growing season. The following table shows expected crop yields and expected contributions towards fixed costs per bushel for each crop: Crop Soybeans Corn Wheat Expected Yield 50 bushels/acre 150 bushels/acre 60 bushels/acre Expected Contribution/Bushel $2 $1 $1.50 The farmer has 400 acres of available land. To facilitate crop rotation, he requires that no single crop be planted on more than half of his land. Also, the farmer has available storage for at most 30,000 bushels of harvested crops. Assume that all of his harvested crops are to be stored at the end of the season, so he must have sufficient storage for his entire anticipated harvest. Formulate a linear program to compute the optimal number of acres to allocate to each crop. 4. (10pt) A farmer is deciding how much corn, soybeans, and wheat to plant in the coming growing season. The following table shows expected crop yields and expected contributions towards fixed costs per bushel for each crop: Crop Soybeans Corn Wheat Expected Yield 50 bushels/acre 150 bushels/acre 60 bushels/acre Expected Contribution/Bushel $2 $1 $1.50 The farmer has 400 acres of available land. To facilitate crop rotation, he requires that no single crop be planted on more than half of his land. Also, the farmer has available storage for at most 30,000 bushels of harvested crops. Assume that all of his harvested crops are to be stored at the end of the season, so he must have sufficient storage for his entire anticipated harvest. Formulate a linear program to compute the optimal number of acres to allocate to each crop.