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rectangular pen is built with one side against a barn. If 300 m of fencing are used for the other three sides of the pen, what dimensions maximize the area 1?

rectangular pen is built with one side against a barn. If 300 m of fencing are used for the other three sides of the pen, what dimensions maximize the area 1?

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 36E
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A rectangular pen is built with one side against a barn. If 300 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of th en? Barn A rancher plans to make four identical and adjacent rectangular pens against a barn, each with an area of 25 m (see figure). hat are the dimensions of each pen that minimize the amount of fence that must be used? 25 25 25 25 Let A be the area of the rectangular pen and let x be the length of the sides perpendicular to the barn. Write the objective function in a form that does not include e length of the side parallel to the barn. Type an expression.) The interval of interest of the objective function is. Simplify your answer. Type your answer in interval notation. Do not use commas in the individual endpoints.) To maximize the area of the pen, the sides perpendicular to the barn should be m long and the side parallel to the barn should be m long. (Type exact answers, using radicals as needed.) b. Let x be the length of the sides perpendicular to the barn and let L be the total length of fence needed. Write the objective function. L-0 (Type an expression.) The interval of interest of the objective function is (1,1) More Enter your answer in each of the answer boxes. NIT
Transcribed Image Text:A rectangular pen is built with one side against a barn. If 300 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of th en? Barn A rancher plans to make four identical and adjacent rectangular pens against a barn, each with an area of 25 m (see figure). hat are the dimensions of each pen that minimize the amount of fence that must be used? 25 25 25 25 Let A be the area of the rectangular pen and let x be the length of the sides perpendicular to the barn. Write the objective function in a form that does not include e length of the side parallel to the barn. Type an expression.) The interval of interest of the objective function is. Simplify your answer. Type your answer in interval notation. Do not use commas in the individual endpoints.) To maximize the area of the pen, the sides perpendicular to the barn should be m long and the side parallel to the barn should be m long. (Type exact answers, using radicals as needed.) b. Let x be the length of the sides perpendicular to the barn and let L be the total length of fence needed. Write the objective function. L-0 (Type an expression.) The interval of interest of the objective function is (1,1) More Enter your answer in each of the answer boxes. NIT
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