a. A rectangular pen is built with one side against a barn. If 200 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of the pen? b. A rancher plans to make four identical and adjacent rectangular pens against a barn, each with an area of 400 m² (see figure). What are the dimensions of each pen that minimize the amount of fence that must be used? C a. To maximize the area of the pen, the sides perpendicular to the barn should be 50 m long and the side parallel to the barn should be 100 m long. (Type exact answers, using radicals as needed.) b. To minimize the amount of fence that must be used, each of the sides perpendicular to the barn should be m long and each of the sides parallel to the barn should be (Type exact answers, using radicals as needed.) Barn 400 400 400 400 m long.
a. A rectangular pen is built with one side against a barn. If 200 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of the pen? b. A rancher plans to make four identical and adjacent rectangular pens against a barn, each with an area of 400 m² (see figure). What are the dimensions of each pen that minimize the amount of fence that must be used? C a. To maximize the area of the pen, the sides perpendicular to the barn should be 50 m long and the side parallel to the barn should be 100 m long. (Type exact answers, using radicals as needed.) b. To minimize the amount of fence that must be used, each of the sides perpendicular to the barn should be m long and each of the sides parallel to the barn should be (Type exact answers, using radicals as needed.) Barn 400 400 400 400 m long.
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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Transcribed Image Text:a. A rectangular pen is built with one side against a barn. If 200 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of the pen?
b. A rancher plans to make four identical and adjacent rectangular pens against a barn, each with an area of 400 m² (see figure). What are the dimensions of each pen that
minimize the amount of fence that must be used?
a. To maximize the area of the pen, the sides perpendicular to the barn should be 50 m long and the side parallel to the barn should be 100 m long.
(Type exact answers, using radicals as needed.)
b. To minimize the amount of fence that must be used, each of the sides perpendicular to the barn should be m long and each of the sides parallel to the barn should be
(Type exact answers, using radicals as needed.)
Barn
400 400 400 400
m long.
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