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A farmer has 300 acres of available land and $60,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c). Profits and Constraints for Crops Potatoes Corn x2 $160 $60 Number of Acres Cost (per acre) Profit (per acre) (a) Give the dual problem. ▼ subject to: X₁ $400 $180 with w=Y₁+Y2 Y₁+400y₂180 Y₁ + 160y₂ Y₁+280/290 Y₁ 20, y₂ 20 60 Cabbage X3 S $280 S $90 = Total 300 $60,000 Z (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 270 acres but capital increases to $63,000. The farmer's estimated profit is $. (Simplify your answer.) (c) Suppose the farmer has 330 acres of land but only $57,000. Find the optimum profit and the planting strategy that will produce this profit. acres of corn, and acres of cabbage will produce an optimal profit of $ Planting acres of potatoes, (Simplify your answers.)

A farmer has 300 acres of available land and $60,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c). Profits and Constraints for Crops Potatoes Corn x2 $160 $60 Number of Acres Cost (per acre) Profit (per acre) (a) Give the dual problem. ▼ subject to: X₁ $400 $180 with w=Y₁+Y2 Y₁+400y₂180 Y₁ + 160y₂ Y₁+280/290 Y₁ 20, y₂ 20 60 Cabbage X3 S $280 S $90 = Total 300 $60,000 Z (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 270 acres but capital increases to $63,000. The farmer's estimated profit is $. (Simplify your answer.) (c) Suppose the farmer has 330 acres of land but only $57,000. Find the optimum profit and the planting strategy that will produce this profit. acres of corn, and acres of cabbage will produce an optimal profit of $ Planting acres of potatoes, (Simplify your answers.)

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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A farmer has 300 acres of available land and $60,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c). Profits and Constraints for Crops Potatoes Corn x2 $160 $60 Number of Acres Cost (per acre) Profit (per acre) (a) Give the dual problem. subject to: X₁ $400 $180 with W = y₁ + Y₁ + 400y2 Y₁ + 160y₂ Y2 180 60 90 Planting acres of potatoes, (Simplify your answers.) Cabbage X3 $280 $90 VI VI II Y₁ + 280y₂ Y₁ ≥ 0, y₂ ≥0 > (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 270 acres but capital increases to $63,000. The farmer's estimated profit is $ (Simplify your answer.) acres of corn, and = Total 300 $60,000 Z (c) Suppose the farmer has 330 acres of land but only $57,000. Find the optimum profit and the planting strategy that will produce this profit. acres of cabbage will produce an optimal profit of $¯.
Transcribed Image Text:A farmer has 300 acres of available land and $60,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c). Profits and Constraints for Crops Potatoes Corn x2 $160 $60 Number of Acres Cost (per acre) Profit (per acre) (a) Give the dual problem. subject to: X₁ $400 $180 with W = y₁ + Y₁ + 400y2 Y₁ + 160y₂ Y2 180 60 90 Planting acres of potatoes, (Simplify your answers.) Cabbage X3 $280 $90 VI VI II Y₁ + 280y₂ Y₁ ≥ 0, y₂ ≥0 > (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 270 acres but capital increases to $63,000. The farmer's estimated profit is $ (Simplify your answer.) acres of corn, and = Total 300 $60,000 Z (c) Suppose the farmer has 330 acres of land but only $57,000. Find the optimum profit and the planting strategy that will produce this profit. acres of cabbage will produce an optimal profit of $¯.
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