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
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I need Help answering both question 5 and 6 . I don’t know how to do them.
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
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