A farmer wants to build a rectangular pen and then divide it with two interior fences. The total area inside of the pen will be 2496 square meters. The exterior fencing costs $18.72 per meter and the interior fencing costs $12.00 per meter. Find the dimensions of the pen that will minimize the cost.
A farmer wants to build a rectangular pen and then divide it with two interior fences. The total area inside of the pen will be 2496 square meters. The exterior fencing costs $18.72 per meter and the interior fencing costs $12.00 per meter. Find the dimensions of the pen that will minimize the cost.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![A farmer wants to build a rectangular pen and then divide it with two interior fences. The total area inside of the pen will be 2496 square meters. The exterior fencing costs $18.72 per meter and the interior fencing costs $12.00 per meter.
Find the dimensions of the pen that will minimize the cost.
### Diagram Explanation
The diagram shows a rectangle representing the pen, with dimensions labeled as follows:
- The horizontal length of the pen is labeled as \( y \).
- The vertical width of the pen is labeled as \( x \).
- Two interior fences divide the pen into three equal sections, each of width \( x \).
### Answer
To find the dimensions:
- \( x = \) [box for answer] meters
- \( y = \) [box for answer] meters](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38cd8332-493e-483a-a0c6-9f0db3571104%2F02b88730-73cb-47fb-addc-268d7d7e8b6a%2Fnj6m4jh_processed.png&w=3840&q=75)
Transcribed Image Text:A farmer wants to build a rectangular pen and then divide it with two interior fences. The total area inside of the pen will be 2496 square meters. The exterior fencing costs $18.72 per meter and the interior fencing costs $12.00 per meter.
Find the dimensions of the pen that will minimize the cost.
### Diagram Explanation
The diagram shows a rectangle representing the pen, with dimensions labeled as follows:
- The horizontal length of the pen is labeled as \( y \).
- The vertical width of the pen is labeled as \( x \).
- Two interior fences divide the pen into three equal sections, each of width \( x \).
### Answer
To find the dimensions:
- \( x = \) [box for answer] meters
- \( y = \) [box for answer] meters
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