Question

Optimization problem:

You need to fence in a rectangular area for a garden outside of your house. One side of the garden is against the wall and does not need a fence. You have 114 feet of fencing material. What are the dimensions of the largest area you can enclose? Draw and label the problem, identify the objective equation, list the constraints, and show all work.

Answer #1

(Optimization Problem) You need to fence in a rectangular area
for a garden outside of your house. One side of the garden is
against the wall and does not need a fence. You have
144 feet of fencing material. What are the
dimensions of the largest area you can enclose? Draw and
label the problem, identify the objective equation, list the
constraints, and show all work.

(Optimization Problem) You're building a fence in a rectangular
area for a garden outside of your house. One side of the garden is
up against the wall of your house and doesn't need fencing. You
have 100 feet of fencing material. What are the
dimensions of the largest area you can enclose? Show all work.

A farmer is building a fence to enclose a rectangular area
against an existing wall, shown in the figure below.
A rectangle labeled, Fenced in Region, is adjacent to a
rectangle representing a wall.
Three of the sides will require fencing and the fourth wall
already exists.
If the farmer has 184 feet of fencing, what is the largest
area the farmer can enclose?

1. You are looking to spruce up your garden by making a
rectangular enclosure using a wall as one side and 160 meters of
fencing for the other three sides. You want to find the dimensions
of the rectangle so that you are maximizing the enclosed area.
(a) Draw and label a picture representing the problem
(b) Write the objective function and the constraint. (You do not
need to label which equation is which.)
(c) Write the area equation in...

You are looking to spruce up your garden by making a rectangular
enclosure using a wall as one side and 120 meters of fencing for
the other three sides. You want to find the dimensions of the
rectangle so that you are maximizing the enclosed area.
(a) Draw and label a picture representing the problem.
(b) Write the objective function and the constraint. (You do not
need to label which equation is which.)
(c) Write the area equation in terms...

(Optimization) A rectangular field is to be fenced off
along a river where no fence is needed on the side along the river.
If the fence for the two ends costs $12/ft and the
fence for the side parallel to the river is
$18/ft. Determine the dimensions of the
field that can be enclosed with the largest possible area. Total
funds available for fencing: $5,400

Suppose that a rectangular garden shall be fenced off and then
divided by a fence into two sections, as pictured below. There is
only 60 feet of fencing for the project. Find the dimensions l and
w of the garden which will maximize the area of the entire
rectangular garden. Be sure to check that these dimensions maximize
the area.

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?

A farmer wants to enclose a rectangular field by a fence and
divide it into 2 smaller but equal rectangular fields by
constructing another fence parallel to one side. He has 6,000 yards
of fencing.(a) draw picture (b) Find the dimensions of the field so
that the total area is a maximum. (c) Find the
dimensions of the rectangular field the farmer can make the will
contain the largest area.

A
fence is to be built to enclose a rectangular area of 800 square
feet. The fence along three sides is to be made of material that
costs $6 per foot. The material for the fourth side costs $18 per
foot. Find the dimensions of the rectangle that will allow for the
most economical fence to be built?

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