5. A rectangular field is to be bounded by a fence on three sides and by a straight stream on the fourth side. Find the dimensions of the field with the maximum area that can be enclosed by 1000 feet of fencing. y RARRRStream = NRRY tep 1: What is the quantity we are trying to maximize?
5. A rectangular field is to be bounded by a fence on three sides and by a straight stream on the fourth side. Find the dimensions of the field with the maximum area that can be enclosed by 1000 feet of fencing. y RARRRStream = NRRY tep 1: What is the quantity we are trying to maximize?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
I need Help answering both question 5 and 6 . I don’t know how to do them.
![5. A rectangular field is to be bounded by a fence on three sides and by a straight
stream on the fourth side. Find the dimensions of the field with the maximum area
that can be enclosed by 1000 feet of fencing.
ER Stream RR
Step 1: What is the quantity we are trying to maximize?
Step 2: What is the formula that relates the variables and the quantity we are trying to
maximize?
Step 3: The amount of fencing is the constraint. Write an equation for this constraint.
Remember that no fencing is needed for the side with the stream.
Step 4: Solve for one of the variables in the constraint equation.
Step 5: Substitute into the function we are trying to maximize, and simplify.
6. An open box is to be made from a sheet which is 30 inches by 30 inches by cutting
out squares of equal size from the four corners and bending up the edges. Let h be
the side of the square. Find the value of h that will produce the large volume.
Write the equation of the function to be maximized. Remember that the volume of a
rectangular solid is V = lwh in terms of h.
V(h) =
cut
fold
30-2h Eh- 30
30-2h
30](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00585539-79e1-42a7-8a75-95bc6de8d9d5%2Fc9483949-e448-40ee-b3c7-a4eb29766b80%2Ftadmfqa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. A rectangular field is to be bounded by a fence on three sides and by a straight
stream on the fourth side. Find the dimensions of the field with the maximum area
that can be enclosed by 1000 feet of fencing.
ER Stream RR
Step 1: What is the quantity we are trying to maximize?
Step 2: What is the formula that relates the variables and the quantity we are trying to
maximize?
Step 3: The amount of fencing is the constraint. Write an equation for this constraint.
Remember that no fencing is needed for the side with the stream.
Step 4: Solve for one of the variables in the constraint equation.
Step 5: Substitute into the function we are trying to maximize, and simplify.
6. An open box is to be made from a sheet which is 30 inches by 30 inches by cutting
out squares of equal size from the four corners and bending up the edges. Let h be
the side of the square. Find the value of h that will produce the large volume.
Write the equation of the function to be maximized. Remember that the volume of a
rectangular solid is V = lwh in terms of h.
V(h) =
cut
fold
30-2h Eh- 30
30-2h
30
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 5 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)