A farmer has 1200 acres of land and plans to plant corn and soybeans. The input cost (cost of seed, fertilizer, herbicide, and insecticide) for 1 acre for each crop is given in the table along with the cost of machinery and labor. The profit for 1 acre of each crop is given in the last column. Input Cost Labor/Machinery per Acre Profit Cost per Acre per Acre Corn $180 $80 $120 Soybeans $120 $100 $100 Suppose the farmer has budgeted a maximum of $198,000 for input costs and a maximum of $110,000 for labor and machinery. a. Determine the number of acres of each crop that the farmer should plant to maximize profit. (Assume that all crops will be sold.) b. What is the maximum profit? c. If the profit per acre were reversed between the two crops (that is, $100 per acre for corn and $120 per acre for soybeans), how many acres of each crop should be planted to maximize profit?
A farmer has 1200 acres of land and plans to plant corn and soybeans. The input cost (cost of seed, fertilizer, herbicide, and insecticide) for 1 acre for each crop is given in the table along with the cost of machinery and labor. The profit for 1 acre of each crop is given in the last column. Input Cost Labor/Machinery per Acre Profit Cost per Acre per Acre Corn $180 $80 $120 Soybeans $120 $100 $100 Suppose the farmer has budgeted a maximum of $198,000 for input costs and a maximum of $110,000 for labor and machinery. a. Determine the number of acres of each crop that the farmer should plant to maximize profit. (Assume that all crops will be sold.) b. What is the maximum profit? c. If the profit per acre were reversed between the two crops (that is, $100 per acre for corn and $120 per acre for soybeans), how many acres of each crop should be planted to maximize profit?
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
Section5.2: Systems Of Linear Equations In Several Variables
Problem 46E
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Transcribed Image Text:A farmer has 1200 acres of land and plans to plant corn and soybeans. The input cost (cost of seed, fertilizer, herbicide,
and insecticide) for 1 acre for each crop is given in the table along with the cost of machinery and labor. The profit for 1
acre of each crop is given in the last column.
Input Cost Labor/Machinery
per Acre
Profit
Cost per Acre
per Acre
Corn
$180
$80
$120
Soybeans
$120
$100
$100
Suppose the farmer has budgeted a maximum of $198,000 for input costs and a maximum of $110,000 for labor and
machinery.
a. Determine the number of acres of each crop that the farmer should plant to maximize profit. (Assume that all crops will
be sold.)
b. What is the maximum profit?
c. If the profit per acre were reversed between the two crops (that is, $100 per acre for corn and $120 per acre for
soybeans), how many acres of each crop should be planted to maximize profit?
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