A farmer has 200 acres of available land and $40,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c) Profits and Constraints for Crops Cabbage Potatoes Corn Total Number of Acres Cost (per acre) Profit (per acre) 200 $400 $120 $160 $40 $280 $60 $40,000 (a) Give the dual problem. Minimize w- 200 y,+ 40000 y2 subject to: Y1400y2 2 120 Y1* 160y2 2 40 Y1* 280y 2 60 Y1 20. y2 20 with (b) The solution to the dual problem can be interpreted as shadow profits. Use shadow profits to estimate the farmer's profitifland is cut to 160 acres but capital increases to $44,000. The farmer's estimated profit is (Simplity your answer.)

A farmer has 200 acres of available land and $40,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c) Profits and Constraints for Crops Cabbage Potatoes Corn Total Number of Acres Cost (per acre) Profit (per acre) 200 $400 $120 $160 $40 $280 $60 $40,000 (a) Give the dual problem. Minimize w- 200 y,+ 40000 y2 subject to: Y1400y2 2 120 Y1* 160y2 2 40 Y1* 280y 2 60 Y1 20. y2 20 with (b) The solution to the dual problem can be interpreted as shadow profits. Use shadow profits to estimate the farmer's profitifland is cut to 160 acres but capital increases to $44,000. The farmer's estimated profit is (Simplity your answer.)

Name: A farmer has 200 acres of available land and $40,000 to spend, He wan
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Description: A farmer has 200 acres of available land and $40,000 to spend, He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c).Profits and Constraints for CropsCabbagePotatoesCornTotalNumber of AcresCost (per ac

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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Question

A farmer has 200 acres of available land and $40,000 to spend, He wants to plant the combination of crops which maximizes his profit. Complete parts (a) through (c).
Profits and Constraints for Crops
Cabbage
Potatoes
Corn
Total
Number of Acres
Cost (per acre)
Profit (per acro)
X2
200
$400
$120
$160
$40
$280
$60
$40,000
(a) Give the dual problem.
Minimize
w= 200 y,+ 40000 y2
subject to: y1 + 400y2 2 120
Y1+ 160y2 2 40
Y1 + 280y2 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 160 acres but capital increases to $44,000.
The farmer's estimated profit is $
(Simplity your answer.)

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