farmer has 300 feet of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is 00 feet. Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions. (Hint: Be mindful of the domain of the function ou are maximizing.) swer Keypa Keyboard Shortc feet by feet

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 Statement:**

A farmer has 300 feet of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is 200 feet. Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions. (Hint: Be mindful of the domain of the function you are maximizing.)

**Solution Explanation:**

To solve this problem, use the given amount of fencing and barn length to determine the optimal dimensions (length and width) that would yield the maximum possible area for the rectangular pen.

**Graphical Explanation:**

The image includes two adjacent blank rectangles where the dimensions of the rectangle (feet by feet) should be specified as the solution to the problem. You will need to use concepts from algebra and calculus, such as setting up a function for the area in terms of one variable and using calculus to find the maximum area within the domain constraints. 

**Important Consideration:**

Keep in mind that the function for area should respect the constraint given by the total amount of fencing (300 feet) and the length of the barn (200 feet) when determining the domain.
Transcribed Image Text:**Problem Statement:** A farmer has 300 feet of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is 200 feet. Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions. (Hint: Be mindful of the domain of the function you are maximizing.) **Solution Explanation:** To solve this problem, use the given amount of fencing and barn length to determine the optimal dimensions (length and width) that would yield the maximum possible area for the rectangular pen. **Graphical Explanation:** The image includes two adjacent blank rectangles where the dimensions of the rectangle (feet by feet) should be specified as the solution to the problem. You will need to use concepts from algebra and calculus, such as setting up a function for the area in terms of one variable and using calculus to find the maximum area within the domain constraints. **Important Consideration:** Keep in mind that the function for area should respect the constraint given by the total amount of fencing (300 feet) and the length of the barn (200 feet) when determining the domain.
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