(a)
To find: The number of acres of each should he plant to earn the greatest profit.
(a)
Answer to Problem 14E
The farmer will use120 acres to be planted with corn and 60 acres to be planted with soybeans.
Explanation of Solution
Given:
An American farmer has 180 acres on which to grow corn and soybeans. He is planting a least 40 acres of corn and 20 acres of soybeans.
If the farmers plants at least 2 acres of corn for every acre of soybeans.
Let
And let
The profit function
The following inequalities must be simultaneously satisfied:
The graph of the above inequalities is given below:
The feasible region is the triangle with vertices
A theorem says that the extreme values of
Further simplified as:
Therefore the farmer will use120 acres to be planted with corn and 60 acres to be planted with soybeans.
(b)
To find: The farmer’s maximum profit.
(b)
Answer to Problem 14E
The maximum profit of farmer will be
Explanation of Solution
It is found that
So the maximum profit of farmer will be
Therefore, the maximum profit of farmer will be
Chapter 2 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Additional Math Textbook Solutions
Calculus: Early Transcendentals (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
University Calculus: Early Transcendentals (4th Edition)
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