Question

A rectangular field is to be enclosed on four sides with a fence. Fencing costs $8 per foot for two opposite sides, and $3 per foot for the other two sides. Find the dimensions of the field of area 870 ft2 that would be the cheapest to enclose.

A) 11.1 ft @ $8 by 78.7 ft @ $3

B) 18.1 ft @ $8 by 48.2 ft @ $3

C) 78.7 ft @ $8 by 11.1 ft @ $3

D) 48.2 ft @ $8 by 18.1 ft @ $3

Answer #1

A rectangular field is to be enclosed on four sides with a
fence. Fencing costs $4 per foot for two opposite sides, and $8 per
foot for the other two sides. Find the dimensions of the field of
area 880 ft 2 that would be the cheapest to enclose.

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 rectangular field is to be enclosed on 4 sides with a fence
with an area of 690 ft². Fencing costs $2 per foot for 2 opposite
sides and $7 per foot for the other 2 sides. The equations for this
question are:
Constraint: xy = 690
Objective: Perimeter (Cost) = 14x + 4y
Find the following:
a) The dimensions that will minimize the cost. Round the
dimensions to 1 decimal place. You may use the rounded dimension to
find...

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
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 $____.

(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

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 has 800 ft of fencing, and wants to fence off a
rectangular field that borders a river with a straight bank. She
needs no fence along the river. What are the dimensions of the
field of largest area?

Two equal rectangular lots are enclosed by fencing the perimeter
of a rectangular lot and then putting a fence across its middle. If
each lot is to contain 2,700 square feet, what is the minimum
amount of fence (in ft) needed to enclose the lots (include the
fence across the middle)?

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

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