Question

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 the other dimension value.**

b) The minimized cost. **Place a $ in your answer and
round it to 2 decimal places.**

Answer #1

we set f'=0 because when function takes maxima or minima then at that point f'=0

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 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...

A rectangular field with one side along a river is to be fenced.
Suppose that no fence is needed along the river, the fence on the
side opposite the river costs $40 per foot, and the fence on the
other sides costs $10 per foot. If the field must contain 72,200
square feet, what dimensions will minimize costs?
side
parallel to the river
ft
each of
the other sides
ft

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 $_

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 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 rectangular field is to have 100 m2 in area. It is
enclosed by a fence. The north-south sides costs $20/m, east-west
sides cost $5/m. What are the dimensions of this fence which
minimizes the total cost?

A fence is to be built to enclose cows in a rectangular area of
200 square feet. The fence along three sides is to be made of
material that costs $5 per foot, and the material for the fourth
side costs $16 dollars per foot. Find the dimensions of the
enclosure that minimize cost, and give the minimum cost to build
the fence

(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

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