Question

Jesse wants to build a rectangular pen for his animals. One side
of the pen will be against the barn; the other three sides will be
enclosed with wire fencing. If Jesse has 700 feet of fencing, what
dimensions would maximize the area of the pen?

a) Let w be the length of the pen perpendicular to the barn. Write
an equation to model the area of the pen in terms of w

Area =

b) What width w would maximize the area?

w =

Answer #1

Ben wants to build a rectangular enclosure for his animals. One
side of the pen will be against the barn, so he needs no fence on
that side. The other three sides will be enclosed with wire
fencing. If Ben has 450 feet of fencing, you can find the
dimensions that maximize the area of the enclosure.
A(W)=A(W)=
b) What width WW would maximize the area?
WW = ft
Round to nearest half foot
c) What is the maximum area?
AA...

1. A rectangular pen is built with one side against a barn. If
600 m of fencing are used for the other three sides of the pen,
complete the following to find the dimensions that maximize the
area of the pen.
True or False: the objective function is the perimeter function,
P=2x+y
2. 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 farmer needs to build a rectangular pen with one side bordered
by a river (that side does not need a fence). He wants the pen to
have an area of 200 sq. ft. What should the dimensions of the pen
be to use the smallest amount of fencing around the three fenced
sides? Support your answer using derivatives

You want to form a rectangular pen of area, a = 60
ft2 (see the figure below). One side of the pen is to be
formed by an existing building and the other three sides by a
fence. If w is the width of the sides of the rectangle
perpendicular to the building, then the length of the side parallel
to the building is L = 60/w. The total amount of
fence required is the function F = 2w +...

We wish to build a rectangular pen. Three of the sides will be
made from standard fencing costing $7 per foot; the fourth side
will be made using a decorative fence costing $19 per foot. If the
total enclosed area must be 1200 sq. ft., what are the dimensions
of the pen with the lowest total cost? What is that total cost?
short side:
long side:
total cost:

A rancher plans to construct a rectangular pen for a cow with an
area of 20 square feet.
Three sides of the pen will be constructed from fencing that costs
$20 per foot of length and the
remaining side will be a stone wall that costs $52 per foot of
length. Find the minimum cost to build
this pen.

A farmer wants to fence in a rectangular plot of land adjacent
to the north wall of his barn. No fencing is needed along the barn,
and the fencing along the west side of the plot is shared with a
neighbor who will split the cost of that portion of the fence. If
the fencing costs $16 per linear foot to install and the farmer is
not willing to spend more than $8000, find the dimensions for the
plot that...

1.) A farmer wants to fence in a rectangular plot of land
adjacent to the north wall of his barn. No fencing is needed along
the barn, and the fencing along the west side of the plot is shared
with a neighbor who will split the cost of that portion of the
fence. If the fencing costs $12 per linear foot to install and the
farmer is not willing to spend more than $3000, find the dimensions
for the plot...

A farmer wants to fence in and area of 1.5 million square feet
in a rectangular field. He then divides the area in half by putting
another line of fencing parallel to one of the sides of the
rectangle in the interior of the area. What is the dimensions of
the rectanglular area that minimizes the amount of fencing used.
Let x denote the length of fencing (in million of ft) along the
direction where 3 pieces of fencing is...

A homeowner wants to create an enclosed rectangular patio area
behind their home. They have 168 feet of fencing to use, and the
side touching the home does not need fence. What should the
dimensions of the patio be to enclose the largest area
possible?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 13 minutes ago

asked 21 minutes ago

asked 24 minutes ago

asked 30 minutes ago

asked 33 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago