7. A farmer has 875 meters of fencing material available to fence a rectangular field. She wants to fence the outside border of the field and then add an additional row of fencing to divide the field into two regions of equal area (see diagram to the right). Use calculus to find the dimensions of the original field that maximize its total area, and then find the maximum area. For credit, show all your supporting work, including a function that represents the total area of ly of the original field

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 7:**

A farmer has 875 meters of fencing material available to fence a rectangular field. She wants to fence the outside border of the field and then add an additional row of fencing to divide the field into two regions of equal area (see diagram to the right). Use calculus to find the dimensions of the original field that maximize its total area, and then find the maximum area. For credit, show all of your supporting work, including a function that represents the total area of the original field.

**Diagram Explanation:**

The diagram shows a rectangle divided into two smaller rectangles by a vertical line. The width of the larger rectangle is labeled as "x," and the height is labeled as "y." This format implies that the fencing creates one long exterior rectangle with an additional internal division along the vertical axis creating two smaller rectangles with width "x" and height "y".
Transcribed Image Text:**Problem 7:** A farmer has 875 meters of fencing material available to fence a rectangular field. She wants to fence the outside border of the field and then add an additional row of fencing to divide the field into two regions of equal area (see diagram to the right). Use calculus to find the dimensions of the original field that maximize its total area, and then find the maximum area. For credit, show all of your supporting work, including a function that represents the total area of the original field. **Diagram Explanation:** The diagram shows a rectangle divided into two smaller rectangles by a vertical line. The width of the larger rectangle is labeled as "x," and the height is labeled as "y." This format implies that the fencing creates one long exterior rectangle with an additional internal division along the vertical axis creating two smaller rectangles with width "x" and height "y".
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