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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 Potatoes Cabbage Total Number of Acres Cost (per acre) Profit (per acre) X2 X3 100 $20,000 $400 $120 $160 $40 $280 $60 %3D (a) Give the dual problem. Minimize w = 100 y, + 20000 y2 subject to: y, +400y, 2 120 Y, + 160y2 2 40 Y, +280y2 2 60 with y, 20, y2 20 (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 80 acres but capital increases to $22,000. The farmer's estimated profit is $ (Simplify your answer.)

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 Potatoes Cabbage Total Number of Acres Cost (per acre) Profit (per acre) X2 X3 100 $20,000 $400 $120 $160 $40 $280 $60 %3D (a) Give the dual problem. Minimize w = 100 y, + 20000 y2 subject to: y, +400y, 2 120 Y, + 160y2 2 40 Y, +280y2 2 60 with y, 20, y2 20 (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 80 acres but capital increases to $22,000. The farmer's estimated profit is $ (Simplify your answer.)

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 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 Potatoes Corn Cabbage Total Number of Acres X1 X2 X3 100 Cost (per acre) Profit (per acre) $400 $120 $160 $40 $280 $60 $20,000 (a) Give the dual problem. Minimize w = 100 y, + 20000 y2 subject to: У1 + 400y, 2 120 У1 + 160y, 2 40 У1 +280y, 2 60 with Y1 20, y2 20 (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 80 acres but capital increases to $22,000. The farmer's estimated profit is $ (Simplify your answer.)
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 Potatoes Corn Cabbage Total Number of Acres X1 X2 X3 100 Cost (per acre) Profit (per acre) $400 $120 $160 $40 $280 $60 $20,000 (a) Give the dual problem. Minimize w = 100 y, + 20000 y2 subject to: У1 + 400y, 2 120 У1 + 160y, 2 40 У1 +280y, 2 60 with Y1 20, y2 20 (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 80 acres but capital increases to $22,000. The farmer's estimated profit is $ (Simplify your answer.)
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