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 minimize the amount of fence that must be used? Bam 100 100 100 100 PN PN
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 minimize the amount of fence that must be used? Bam 100 100 100 100 PN PN
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.4: Polyhedrons And Spheres
Problem 23E: The surface of a soccer ball is composed of 12 regular pentagons and 20 regular hexagons. With each...
Related questions
Question
![a. Arectangular 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
PN pen?
Bam
(see figure).
PN
b. Arancher plans to make four identical and
PN
What are the dimensions of each pen that minimize the amount of fence that must be used?
adjacent rectangular pens against a barn, each with an area of 100 m
100
100
100
100
PN
PN
PN
a. 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
PN
the length of the side parallel to the barn.
PN
2.
A= 2500x-2x
PN (Type an expression.)
PN
PN
The interval of interest of the objective function is [0, 1250]
PN
(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 625 m long and the side parallel to the barn should be 1250 m long.
JPG
(Type exact answers, using radicals as needed.)
JPG
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.
7 PM
JPd
400
L=\5x+
JPG
(Type an expression.)
35 PM
17 PM
JPd
5:20 PM
JP The interval of interest of the objective function is (0, co)
2:59 PM
JPO (Simplify your answer. Type your answer in interval notation. Do not use commas in the individual endpoints.)
1:57 PM
JPG
Enter your answer in each of the answer boxes.
9 1:46 PM
JPO
19 1:32 PM
JPC
019 1:29 PM
JPG
019 1:25 PM
JPG File
1,437 KB
33 nI
Custom Files
Open
Cancel
SAMPLE
METHYST
8/23/2020 (BAJ)
8920362898
NOT RETURNABLE](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d5052ba-2cef-40d4-b4e2-378bd356ffd9%2Fc67267bf-8eef-4b85-8831-08d7fc2df9dc%2Fxh9l4pd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a. Arectangular 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
PN pen?
Bam
(see figure).
PN
b. Arancher plans to make four identical and
PN
What are the dimensions of each pen that minimize the amount of fence that must be used?
adjacent rectangular pens against a barn, each with an area of 100 m
100
100
100
100
PN
PN
PN
a. 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
PN
the length of the side parallel to the barn.
PN
2.
A= 2500x-2x
PN (Type an expression.)
PN
PN
The interval of interest of the objective function is [0, 1250]
PN
(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 625 m long and the side parallel to the barn should be 1250 m long.
JPG
(Type exact answers, using radicals as needed.)
JPG
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.
7 PM
JPd
400
L=\5x+
JPG
(Type an expression.)
35 PM
17 PM
JPd
5:20 PM
JP The interval of interest of the objective function is (0, co)
2:59 PM
JPO (Simplify your answer. Type your answer in interval notation. Do not use commas in the individual endpoints.)
1:57 PM
JPG
Enter your answer in each of the answer boxes.
9 1:46 PM
JPO
19 1:32 PM
JPC
019 1:29 PM
JPG
019 1:25 PM
JPG File
1,437 KB
33 nI
Custom Files
Open
Cancel
SAMPLE
METHYST
8/23/2020 (BAJ)
8920362898
NOT RETURNABLE
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning