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A farmer has 100 acres of available land and $20,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c). Profits and Constraints for Crops Corn Cabbage Potatoes Total Number of Acres X3 $224 $90 X1 100 X2 $128 Cost (per acre) Profit (per acre) $320 $20,000 $180 $60 %3D Maximize %3D subject to: y1 +320y2 2 y, + 128y2 2 Y1 +224y2 2 y, 20, y2 20 with (Simplify your answers. Do not factor.) (b) The solution to the dual problem can be interpreted as shadow profits. Use shadow profits to estimate the farmer's profit if land is cut to 90 acres but capital increases to $21,000. The farmer's estimated profit is $ (Type an integer or a decimal.) (c) Suppose the farmer has 110 acres of land but only $19,000. Find the optimum profit and the planting strategy that will produce this profit. Planting acres of potatoes, acres of corn, and acres of cabbage will produce an optimal profit of $ (Type integers or decimals.)

A farmer has 100 acres of available land and $20,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c). Profits and Constraints for Crops Corn Cabbage Potatoes Total Number of Acres X3 $224 $90 X1 100 X2 $128 Cost (per acre) Profit (per acre) $320 $20,000 $180 $60 %3D Maximize %3D subject to: y1 +320y2 2 y, + 128y2 2 Y1 +224y2 2 y, 20, y2 20 with (Simplify your answers. Do not factor.) (b) The solution to the dual problem can be interpreted as shadow profits. Use shadow profits to estimate the farmer's profit if land is cut to 90 acres but capital increases to $21,000. The farmer's estimated profit is $ (Type an integer or a decimal.) (c) Suppose the farmer has 110 acres of land but only $19,000. Find the optimum profit and the planting strategy that will produce this profit. Planting acres of potatoes, acres of corn, and acres of cabbage will produce an optimal profit of $ (Type integers or decimals.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A farmer has 100 acres of available land and $20,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c). Profits and Constraints for Crops Corn Cabbage Potatoes Total Number of Acres X3 $224 $90 X1 X2 100 Cost (per acre) Profit (per acre) $320 $128 $20,000 $180 $60 %3D Maximize subject to: y1 +320y2 2 y, + 128y2 2 Y1 +224y2 2 Y, 20, Y2 20 with (Simplify your answers. Do not factor.) (b) The solution to the dual problem can be interpreted as shadow profits. Use shadow profits to estimate the farmer's profit if land is cut to 90 acres but capital increases to $21,000. The farmer's estimated profit is $ (Type an integer or a decimal.) (c) Suppose the farmer has 110 acres of land but only $19,000. Find the optimum profit and the planting strategy that will produce this profit. Planting acres of potatoes, acres of corm, and acres of cabbage will produce an optimal profit of $ (Type integers or decimals.)
Transcribed Image Text:A farmer has 100 acres of available land and $20,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c). Profits and Constraints for Crops Corn Cabbage Potatoes Total Number of Acres X3 $224 $90 X1 X2 100 Cost (per acre) Profit (per acre) $320 $128 $20,000 $180 $60 %3D Maximize subject to: y1 +320y2 2 y, + 128y2 2 Y1 +224y2 2 Y, 20, Y2 20 with (Simplify your answers. Do not factor.) (b) The solution to the dual problem can be interpreted as shadow profits. Use shadow profits to estimate the farmer's profit if land is cut to 90 acres but capital increases to $21,000. The farmer's estimated profit is $ (Type an integer or a decimal.) (c) Suppose the farmer has 110 acres of land but only $19,000. Find the optimum profit and the planting strategy that will produce this profit. Planting acres of potatoes, acres of corm, and acres of cabbage will produce an optimal profit of $ (Type integers or decimals.)
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