A rectangular fence enclosing 32 ft² is to be built. The north and south sides are built using material that costs $1 per ft. The material for the west and east sides costs $2 per ft. Let z ft be the length of the north (and also south) side. Let y ft be the length of the west (and also east) side. (1) Find y as a function of 2. y = (2) Find the cost of building the fence as a function of x. Your answer should be in terms of only. f(x) = (3) Find the interval for z. Use oo if necessary. < I< (4) Find the dimensions that minimize the cost of the fence. (In quizzes and tests, you will need to explain why the value of a you have found gives the minimum cost.) The length of the north and south sides is: The length of the west and east sides is: ft ft
A rectangular fence enclosing 32 ft² is to be built. The north and south sides are built using material that costs $1 per ft. The material for the west and east sides costs $2 per ft. Let z ft be the length of the north (and also south) side. Let y ft be the length of the west (and also east) side. (1) Find y as a function of 2. y = (2) Find the cost of building the fence as a function of x. Your answer should be in terms of only. f(x) = (3) Find the interval for z. Use oo if necessary. < I< (4) Find the dimensions that minimize the cost of the fence. (In quizzes and tests, you will need to explain why the value of a you have found gives the minimum cost.) The length of the north and south sides is: The length of the west and east sides is: ft ft
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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Transcribed Image Text:A rectangular fence enclosing 32 ft2 is to be built. The north and south sides are built using material that
costs $1 per ft. The material for the west and east sides costs $2 per ft.
Let z ft be the length of the north (and also south) side. Let y ft be the length of the west (and also east)
side.
(1) Find y as a function of 2.
y =
(2) Find the cost of building the fence as a function of x. Your answer should be in terms of only.
f(x) =
(3) Find the interval for x. Use co if necessary.
< x <
(4) Find the dimensions that minimize the cost of the fence. (In quizzes and tests, you will need to explain
why the value of a you have found gives the minimum cost.)
The length of the north and south sides is:
The length of the west and east sides is:
ft
ft
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