Problem 3 (30 points) Farmer Dave can grow a combination of corn, sorghum and wheat. For inputs, he uses land, labor, and fertilizer of which he has endowments of 350 acres, 500 hours, and 300 bags, respectively. He has family labor hours of 6,000 and can hire up to an additional 450 hours of hired labor at a cost of $5.00 per hour. Production Operatic Labor Requirement Variable Cost Fertilizer Usage Yields/Prices Plow 0.5 hours/acre 10 $/acre Disk 0.5 hours/acre 10 $/acre Plant Corn 0.3 hours/acre 75 $/acre 0.70 bags/acre Plant Sorghum 0.3 hours/acre 45 $/acre 0.57 bags/acre Plant Wheat 0.3 hours/acre 40 $/acre 0.67 bags/acre Harvest Corn 1.35 hours/acre 50 S/acre 125 bu/acre Harvest Sorghum 0.75 hours/acre 25 S/acre 82 bu/acre Harvest Wheat 0.6 hours/acre 44 S/acre 41 bu/acre Corn Price 3.55 $/bu Sorghum Price 3.75 $/bu Wheat Price 4.95 $/bu Suppose Dave now has an option to expand his crop farm to a livestock-crop enterprise. He wants to evaluate whether or not it is worth of adding up to 50 dairy cows to his farm. Assume that the cost per cow is $500, and each cow can produce 15,500 pounds of milk per year. The expected price for milk is $0.14 per pound. Each cow requires the following annual diet produced entirely on the land owned by Dave: (1) a concentrate made out of 35 bushels of corn mixed with 9 bushels of soybeans, and (2) 1.22 tons of hay. Thus, Dave needs to grow hay in addition to corn, sorghum and wheat. The expected yield of hay is 2.5 tons per acre with a cost of $15 per acre for planting hay and $16 per acre for harvesting hay. Dave will apply 0.35 bags of fertilizer per bag. The required labor hours for planting and harvesting hay is 0.25 hours and 0.50 hours per acre, respectively. The labor for milking cows is 65 hours per cow. The hay beyond the need of the dairy herd can be sold to the market for $75.00 per ton. Formulate the LP model for this problem. [Just for the case with dairy cowl Solve it with Spreadsheet modeling You need to set two separate models: with- and without dairy cow] What's your recommendation to Farmer Dave? supply function for corn, wheat and milk (under the with dairy cow case] d. Derive a supply function for corn, wheat an demand function for land and labor (under the with dairy cow case] e. Derive a demand function for lan Problem 3 (30 points) Farmer Dave can grow a combination of corn, sorghum and wheat. For inputs, he uses land, labor, and fertilizer of which he has endowments of 350 acres, 500 hours, and 300 bags, respectively. He has family labor hours of 6,000 and can hire up to an additional 450 hours of hired labor at a cost of $5.00 per hour. Production Operatic Labor Requirement Variable Cost Fertilizer Usage Yields/Prices Plow 0.5 hours/acre 10 $/acre Disk 0.5 hours/acre 10 $/acre Plant Corn 0.3 hours/acre 75 $/acre 0.70 bags/acre Plant Sorghum 0.3 hours/acre 45 $/acre 0.57 bags/acre Plant Wheat 0.3 hours/acre 40 $/acre 0.67 bags/acre Harvest Corn 1.35 hours/acre 50 S/acre 125 bu/acre Harvest Sorghum 0.75 hours/acre 25 S/acre 82 bu/acre Harvest Wheat 0.6 hours/acre 44 S/acre 41 bu/acre Corn Price 3.55 $/bu Sorghum Price 3.75 $/bu Wheat Price 4.95 $/bu Suppose Dave now has an option to expand his crop farm to a livestock-crop enterprise. He wants to evaluate whether or not it is worth of adding up to 50 dairy cows to his farm. Assume that the cost per cow is $500, and each cow can produce 15,500 pounds of milk per year. The expected price for milk is $0.14 per pound. Each cow requires the following annual diet produced entirely on the land owned by Dave: (1) a concentrate made out of 35 bushels of corn mixed with 9 bushels of soybeans, and (2) 1.22 tons of hay. Thus, Dave needs to grow hay in addition to corn, sorghum and wheat. The expected yield of hay is 2.5 tons per acre with a cost of $15 per acre for planting hay and $16 per acre for harvesting hay. Dave will apply 0.35 bags of fertilizer per bag. The required labor hours for planting and harvesting hay is 0.25 hours and 0.50 hours per acre, respectively. The labor for milking cows is 65 hours per cow. The hay beyond the need of the dairy herd can be sold to the market for $75.00 per ton. Formulate the LP model for this problem. [Just for the case with dairy cowl Solve it with Spreadsheet modeling You need to set two separate models: with- and without dairy cow] What's your recommendation to Farmer Dave? supply function for corn, wheat and milk (under the with dairy cow case] d. Derive a supply function for corn, wheat an demand function for land and labor (under the with dairy cow case] e. Derive a demand function for lan
