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A farmer has 100 feet of fence with which he plans to enclose a rectangular pen along one side of his barn. One side of the pen is the barn wall. The fencing will construct the remaining 3 sides. What are the dimensions of the pen to maximize the area?

A farmer has 100 feet of fence with which he plans to enclose a rectangular pen along one side of his barn. One side of the pen is the barn wall. The fencing will construct the remaining 3 sides. What are the dimensions of the pen to maximize the area?

Calculus: Early Transcendentals
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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**Problem 5:** A farmer has 100 feet of fence with which he plans to enclose a rectangular pen along one side of his barn. One side of the pen is the barn wall. The fencing will construct the remaining 3 sides. What are the dimensions of the pen to maximize the area? --- This problem involves understanding how to optimize the dimensions of a rectangular enclosure using a fixed amount of fencing. Only three sides of the rectangle need fencing because the barn wall serves as the fourth side. The task is to find the optimal dimensions of the rectangle that provide the maximum enclosed area.
Transcribed Image Text:**Problem 5:** A farmer has 100 feet of fence with which he plans to enclose a rectangular pen along one side of his barn. One side of the pen is the barn wall. The fencing will construct the remaining 3 sides. What are the dimensions of the pen to maximize the area? --- This problem involves understanding how to optimize the dimensions of a rectangular enclosure using a fixed amount of fencing. Only three sides of the rectangle need fencing because the barn wall serves as the fourth side. The task is to find the optimal dimensions of the rectangle that provide the maximum enclosed area.
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