Please show work using matrices, thank you! A farmer has 400 acres of available land and $80,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts a. through c.belowNumber of AcresCost (per acre)Profit (per acre)a. Give the quai propiem▼subject towithProfits and Constraints for CropsPotatoesCornX₂$128$40W=X1$320$120Y₁ + 320y₂Y₁ + 128y2Y₁ +224y₂Y₁ 20, y₂ 20₂12040▼60CabbageX3$224$60Total400$80,000b. 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 360 acres but capitalincreases to $84,000.The farmer's estimated profit is $c. Suppose the farmer has 440 acres of land but only $76,000. Find the optimum profit and the planting strategy that will produce this profit.Planting acres of potatoes,acres of com, andacres of cabbage will produce an optimal profit of $*

Objective Functions and Constraints:Based on the given details, the objective functions and…

A farmer has 400 acres of available land and $80,000 to spend. He wants to plant the combination of crops which 'maximizes his profit. Complete parts a. through c. below Number of Acres Cost (per acre) Profit (per acre) a. Give the quai propiem ▼ subject to Profits and Constraints for Crops Potatoes W= 21 $320 $120 Y₁ +320y2 Y₁ + 128y2 ₂ 120 40 Corn X₂ $128 $40 Cabbage X3 $224 $60 Total 400 $80,000 *

A farmer has 400 acres of available land and $80,000 to spend. He wants to plant the combination of crops which 'maximizes his profit. Complete parts a. through c. below Number of Acres Cost (per acre) Profit (per acre) a. Give the quai propiem ▼ subject to Profits and Constraints for Crops Potatoes W= 21 $320 $120 Y₁ +320y2 Y₁ + 128y2 ₂ 120 40 Corn X₂ $128 $40 Cabbage X3 $224 $60 Total 400 $80,000 *

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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Question

Please show work using matrices, thank you!

A farmer has 400 acres of available land and $80,000 to spend. He wants to plant the combination of crops which maximizes his profit. Complete parts a. through c.
below
Number of Acres
Cost (per acre)
Profit (per acre)
a. Give the quai propiem
▼
subject to
with
Profits and Constraints for Crops
Potatoes
Corn
X₂
$128
$40
W=
X1
$320
$120
Y₁ + 320y₂
Y₁ + 128y2
Y₁ +224y₂
Y₁ 20, y₂ 20
₂
120
40
▼60
Cabbage
X3
$224
$60
Total
400
$80,000
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 360 acres but capital
increases to $84,000.
The farmer's estimated profit is $
c. Suppose the farmer has 440 acres of land but only $76,000. Find the optimum profit and the planting strategy that will produce this profit.
Planting acres of potatoes,
acres of com, and
acres of cabbage will produce an optimal profit of $
*

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