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 Potatoes Corn Number of Acres Cost (per acre) X₁ $320 $128 Cabbage x₂ $324 S Total 500 $100.000
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 Potatoes Corn Number of Acres Cost (per acre) X₁ $320 $128 Cabbage x₂ $324 S Total 500 $100.000
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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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
Potatoes
Corn
Number of Acres
Cost (per acre)
Profit (per acre)
X₁
$320
$120
with
Minimize
subject to: y₁ +320y₂ 2 120.
Y₁+1282 2 40
w = 500 y₁ + 100000 ₂
Y₁+224y > 60
Y₁ 20, y₂ 20
$128
$40
The farmer's estimated profit is $
(Simplity your answer.)
Cabbage
X3
$224
$60
S
≤
=
Total
500
$100,000
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 400 acres but capital increases to
$110,000.
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