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a. To maximize the area of the pen, the sides perpendicular to the barn should be 625 m long and the side parallel to the barn should be 1250 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 m long. (Type exact answers, using radicals as needed.)

a. To maximize the area of the pen, the sides perpendicular to the barn should be 625 m long and the side parallel to the barn should be 1250 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 m long. (Type exact answers, using radicals as needed.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 26EQ
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Solve part B.

a. A rectangular pen is built with one side against a barn. If 2500 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 100 m (see figure). What are the dimensions of each pen that Barn minimize the amount of fence that must be used? 100 100 100 | 100 a. To maximize the area of the pen, the sides perpendicular to the barn should be 625 m long and the side parallel to the barn should be 1250 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 m long. (Type exact answers, using radicals as needed.)
Transcribed Image Text:a. A rectangular pen is built with one side against a barn. If 2500 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 100 m (see figure). What are the dimensions of each pen that Barn minimize the amount of fence that must be used? 100 100 100 | 100 a. To maximize the area of the pen, the sides perpendicular to the barn should be 625 m long and the side parallel to the barn should be 1250 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 m long. (Type exact answers, using radicals as needed.)
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