Wilson Creek Farm has 200 acres of land available for planting. The owner is considering planting three crops: corn, soybeans, and wheat. The production yield, water requirements, and labor requirements for a salable crop are given here. The owner expects to have only 35,000 gallons of water available per week to use for the crops, and during the growing season he will only have 8000 person-hours of labor available. The expected profit per bushel of each crop is $1.00 for corn, $1.60 for soybeans, and $3.00 for wheat. The owner can use any mix of crops (i.e., he can plant the same crop on all 200 acres or he can plant all three crops in different proportions). b. Formulate the problem as a linear program to find the profit-maximizing planting strategy.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Problem 33P: Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand...
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Wilson Creek Farm has 200 acres of land available for planting. The owner is considering planting three
crops: corn, soybeans, and wheat. The production yield, water requirements, and labor requirements for
a salable crop are given here. The owner expects to have only 35,000 gallons of water available per week
to use for the crops, and during the growing season he will only have 8000 person-hours of labor available.
The expected profit per bushel of each crop is $1.00 for corn, $1.60 for soybeans, and $3.00 for wheat.
The owner can use any mix of crops (i.e., he can plant the same crop on all 200 acres or he can plant all
three crops in different proportions).
b. Formulate the problem as a linear program to find the profit-maximizing planting strategy.
Crop
Corn
Soybeans
Wheat
Bushels/ Acre
Produced
300
200
80
Water Required
(gal/acre/week)
200
150
125
Person-Hours Labor
Required/Acre
35
40
30
Transcribed Image Text:Wilson Creek Farm has 200 acres of land available for planting. The owner is considering planting three crops: corn, soybeans, and wheat. The production yield, water requirements, and labor requirements for a salable crop are given here. The owner expects to have only 35,000 gallons of water available per week to use for the crops, and during the growing season he will only have 8000 person-hours of labor available. The expected profit per bushel of each crop is $1.00 for corn, $1.60 for soybeans, and $3.00 for wheat. The owner can use any mix of crops (i.e., he can plant the same crop on all 200 acres or he can plant all three crops in different proportions). b. Formulate the problem as a linear program to find the profit-maximizing planting strategy. Crop Corn Soybeans Wheat Bushels/ Acre Produced 300 200 80 Water Required (gal/acre/week) 200 150 125 Person-Hours Labor Required/Acre 35 40 30
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