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A farmer has 500 acres of available land and $100,000 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 $224 500 $320 $128 3 $100,000 $120 $40 $60 (a) Give the dual problem. w = 500y, + 100000y2 y, + 320y2 2 120 y, + 128y2 2 40 y, + 224y2 2 60 y, 2 0, Y2 z 0 (Simplify your answers. Do not factor.) Minimize subject to: with (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 450 acres but capital increases to $105,000 The farmer's estimated profit is s (Type an integer or a decimal.) (c) Suppose the farmer has 550 acres of land but only $95,000. Find the optimum profit and the planting strategy that will produce this profit. Planting O acres of potatoes, (Type integers or decimals.) acres of corn, and acres of cabbage will produce an optimal profit of S.

A farmer has 500 acres of available land and $100,000 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 $224 500 $320 $128 3 $100,000 $120 $40 $60 (a) Give the dual problem. w = 500y, + 100000y2 y, + 320y2 2 120 y, + 128y2 2 40 y, + 224y2 2 60 y, 2 0, Y2 z 0 (Simplify your answers. Do not factor.) Minimize subject to: with (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 450 acres but capital increases to $105,000 The farmer's estimated profit is s (Type an integer or a decimal.) (c) Suppose the farmer has 550 acres of land but only $95,000. Find the optimum profit and the planting strategy that will produce this profit. Planting O acres of potatoes, (Type integers or decimals.) acres of corn, and acres of cabbage will produce an optimal profit of S.

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 500 acres of available land and $100,000 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 X1 $320 X2 $128 X3 $224 500 s $100,000 Cost (per acre) Profit (per acre) $120 $40 $60 = (a) Give the dual problem. Minimize w = 500y, + 100000y2 y, + 320y2 2 y, + 128y2 2 y, + 224y2 2 60 y, 2 0, y2 20 subject to: 120 40 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 450 acres but capital increases to $105,000. The farmer's estimated profit is $ (Type an integer or a decimal.) (c) Suppose the farmer has 550 acres of land but only $95,000. Find the optimum profit and the planting strategy that will produce this profit. Planting acres of potatoes, (Type integers or decimals.) acres of com, and acres of cabbage will produce an optimal profit of $
Transcribed Image Text:A farmer has 500 acres of available land and $100,000 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 X1 $320 X2 $128 X3 $224 500 s $100,000 Cost (per acre) Profit (per acre) $120 $40 $60 = (a) Give the dual problem. Minimize w = 500y, + 100000y2 y, + 320y2 2 y, + 128y2 2 y, + 224y2 2 60 y, 2 0, y2 20 subject to: 120 40 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 450 acres but capital increases to $105,000. The farmer's estimated profit is $ (Type an integer or a decimal.) (c) Suppose the farmer has 550 acres of land but only $95,000. Find the optimum profit and the planting strategy that will produce this profit. Planting acres of potatoes, (Type integers or decimals.) acres of com, and acres of cabbage will produce an optimal profit of $
Need b) and c) please
Transcribed Image Text:Need b) and c) please
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