Question

Use the method of Lagrange multipliers to solve this exercise. I want to fence in a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. I have a budget of $96 for the project.

What is the largest area I can enclose? ft2

Answer #1

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Use the method of Lagrange multipliers to solve this
exercise.
I want to fence in a rectangular vegetable patch. The fencing
for the east and west sides costs $6 per foot, and the fencing for
the north and south sides costs only $3 per foot. I have a budget
of $120 for the project. What is the largest area I can
enclose?
Please find answer (show steps) and will rate!

I would like to create a rectangular vegetable patch. The
fencing for the east and west sides costs $4 per foot, and the
fencing for the north and south sides costs only $2 per foot. I
have a budget of $128 for the project. What are the dimensions of
the vegetable patch with the largest area I can enclose?
north and south sides= ?
east and west sides = ?

I would like to create a rectangular vegetable patch. The
fencing for the east and west sides costs $4 per foot, and the
fencing for the north and south sides costs only $2 per foot. I
have a budget of $176 for the project. What are the dimensions of
the vegetable patch with the largest area I can enclose? HINT [See
Example 2.].
North East sides =
East and West sides =

For tax reasons, I need to create a rectangular vegetable patch
with an area of exactly 98 square feet. The fencing for the east
and west sides costs $4 per foot, and the fencing for the north and
south sides costs only $2 per foot. What are the dimensions of the
vegetable patch with the least expensive fence?
north and south sides ft
east and west
sides ft

For tax reasons, I need to create a rectangular vegetable patch
with an area of exactly 200 square feet. The fencing for the east
and west sides costs $4 per foot, and the fencing for the north and
south sides costs only $2 per foot. What are the dimensions of the
vegetable patch with the least expensive fence?
north and south sides fteast and west sides ft

Solve the problem.
A rectangular field is to be enclosed on four sides with a fence.
Fencing costs $2 per foot for two opposite sides, and $7 per foot
for the other two sides. Find the dimensions of the field of area
610 ft2 that would be the cheapest to enclose.

A fence must be built to enclose a rectangular area of
20,000ft2. Fencing material costs $1 per foot for the
two sides facing north and south and $2 per foot for the other two
sides. Find the cost of the least expensive fence.
The cost of the least expensive fence is $____.

A
fence must be built to enclose a rectangular area of 5000 ft^2.
Fencing material costs $4 per foot for the two sides facing north
and south and $8 per foot for the other two sides. Find the cost of
the least expensive fence.
The cost of the least expensive fence is $_

A fence must be built to enclose a rectangular area of 140,000
m2. Fencing material costs $7 per metre for the two
sides facing north and south, and $4 per metre for the other two
sides. Find the cost of the least expensive fence. Justify your
result.

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 fencing along the west side of the plot is shared with a
neighbor who will split the cost of that portion of the fence.
Fencing costs $20 per linear foot. The farmer is not willing to
spend more than $5000. Find the dimension for the plot that would
enclose the most area.

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