Suppose you, as a young entrepreneur, are starting a small poultry business. Your parents have provided you with a 40-meter-long cyclone wire that is 3 meters high enough to enclose the chickens in the backyard. You want to maximize the area of the chicken pen and you want the pen to be rectangular. What must be the dimensions of the chicken pen so the area will be maximized Considering the given situation, answer the following: 1. What is the given perimeter of the pen? (In meters) 2. Let x be the length of the pen. Express the width of the pen in terms of x. (in meters) 3. Express the area of the rectangular pen, y, as a function of x. (in sqm)

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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Solve the following problem and SHOW YOUR COMPLETE SOLUTIONS FOR BETTER UBDERSTANDING
Solve the following problem and show your complete solutions:
Suppose you, as a young entrepreneur, are starting a small poultry business.
Your parents have provided you with a 40-meter-long cyclone wire that is 3
meters high enough to enclose the chickens in the backyard.
You want to maximize the area of the chicken pen and you want the pen to be
rectangular. What must be the dimensions of the chicken pen so the area will
be maximized
Considering the given situation, answer the following:
1. What is the given perimeter of the pen? (In meters)
2. Let x be the length of the pen. Express the width of the pen in terms of x. (in
meters)
3. Express the area of the rectangular pen, y, as a function of x. (in sqm)
4. What is the domain of the function?
5. What is the range of the function?
6. What is the area of the pen if the fence is 4 meters long?
7. What is the area of the pen if the fence is 5 meters long?
8. What is the area of the pen if the fence is 15 meters long?
9. What is the area of the pen if the fence is 16 meters long?
10. Is it possible for the fence to be 30? Why?
Transcribed Image Text:Solve the following problem and show your complete solutions: Suppose you, as a young entrepreneur, are starting a small poultry business. Your parents have provided you with a 40-meter-long cyclone wire that is 3 meters high enough to enclose the chickens in the backyard. You want to maximize the area of the chicken pen and you want the pen to be rectangular. What must be the dimensions of the chicken pen so the area will be maximized Considering the given situation, answer the following: 1. What is the given perimeter of the pen? (In meters) 2. Let x be the length of the pen. Express the width of the pen in terms of x. (in meters) 3. Express the area of the rectangular pen, y, as a function of x. (in sqm) 4. What is the domain of the function? 5. What is the range of the function? 6. What is the area of the pen if the fence is 4 meters long? 7. What is the area of the pen if the fence is 5 meters long? 8. What is the area of the pen if the fence is 15 meters long? 9. What is the area of the pen if the fence is 16 meters long? 10. Is it possible for the fence to be 30? Why?
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