A farmer is going to divide her 60 acre farm between two crops. Seed for crop A costs $5 per acre. Seed for Crop B costs $10 per acre. The farmer can spend at most $450 on seed. If crop B brings in a profit of $100 per acre, and crop A brings in a profit of $130 per acre , how many acres of each crop should the farmer plant to maximize her profit?
A farmer is going to divide her 60 acre farm between two crops. Seed for crop A costs $5 per acre. Seed for Crop B costs $10 per acre. The farmer can spend at most $450 on seed. If crop B brings in a profit of $100 per acre, and crop A brings in a profit of $130 per acre , how many acres of each crop should the farmer plant to maximize her profit?
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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A farmer is going to divide her 60 acre farm between two crops. Seed for crop A costs $5 per acre. Seed for Crop B costs $10 per acre. The farmer can spend at most $450 on seed. If crop B brings in a profit of $100 per acre, and crop A brings in a profit of $130 per acre , how many acres of each crop should the farmer plant to maximize her profit?
Expert Solution
Step 1
Let the crop A is planted on x acres
and crop B is planted on y acres
therefore,
cost will give the constraints as
The objective is to maximise the profit therefore,
therefore, the LPP is
subject to
where
use the graphical method to solve the LPP
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