Question

A 10 ft3 capacity rectangular box with open top is to be constructed so that the length of the base of the box will be twice as long as its width. The material for the bottom of the box costs 20 cents per square foot and the material for the sides of the box costs 10 cents per square foot. Find the dimensions of the least expensive box that can be constructed.

Answer #1

A rectangular box is to have a square base and a volume of 48
ft3. If the material for the base costs 4 cents per square foot,
material for the top costs 20 cents per square foot, and the
material for the sides costs 16 cents per square foot, determine
the dimensions of the square base (in feet) that minimize the total
cost of materials used in constructing the rectangular box.

A rectangular box is to have a square base and a volume of 45
ft3. If the material for the base costs 14 cents per square foot,
material for the top costs 6 cents per square foot, and the
material for the sides costs 6 cents per square foot, determine the
dimensions of the square base (in feet) that minimize the total
cost of materials used in constructing the rectangular box.

A rectangular box is to have a square base and a volume of 16
ft3. If the material for the base costs
$0.14/ft2, the material for the sides costs
$0.06/ft2, and the material for the top costs
$0.10/ft2, determine the dimensions (in ft) of the box
that can be constructed at minimum cost. (Refer to the figure
below.)
A closed rectangular box has a length of x, a width of
x, and a height of y.

A rectangular box with a volume of 272 ft. cubed is to be
constructed with a square base and top. The cost per square foot
for the bottom is15cents, for the top is10cents, and for the other
sides is 2.5 cents. What dimensions will minimize the cost?
What are the dimensions of the box?
The length of on side of the base is ___
The height of the box is___ (Rounds to one decimal place as
needed)

A pencil cup with a capacity of 48 in^3 is to be constructed in
the shape of a rectangular box with a square base and an open top.
If the material for the sides costs 40¢/in^2 and the material for
the base costs 60¢/in.^2, what should the dimensions of the cup be
to minimize the construction cost? A pencil cup is in the shape of
a rectangular box with a square base and an open top.
height ____ in
length...

Minimizing Costs A pencil cup with a capacity of 45 in.^3 is to
be constructed in the shape of a rectangular box with a square base
and an open top. If the material for the sides costs 27¢/in.^2 and
the material for the base costs 90¢/in.^2, what should the
dimensions of the cup be to minimize the construction cost? A
pencil cup is in the shape of a rectangular box with a square base
and an open top.
height
length...

An open-top rectangular box is being constructed to hold a
volume of 300 in3. The base of the box is made from a
material costing 8 cents/in2. The front of the box must
be decorated, and will cost 12 cents/in2. The remainder
of the sides will cost 2 cents/in2.
Find the dimensions that will minimize the cost of constructing
this box.
Front width: _______ in.
Depth: ________ in.
Height: ________ in.

Find the dimensions and volume of the box of maximum volume that
can be constructed. The rectangular box having a top and a square
base is to be constructed at a cost of $4. If the material for the
bottom costs $0.10 per square foot, the material for the top costs
$0.35 per square foot, and the material for the sides costs $0.25
per square foot,

A rectangular storage container with an open top is to have a
volume of 10 m3. The length of this base is twice the width.
Material for the base costs $10 per square meter. Material for the
sides costs $6 per square meter. Find the cost of materials for the
cheapest such container. (Round your answer to the nearest cent.)A
rectangular storage container with an open top is to have a volume
of 10 m3. The length of this base...

A rectangular box is to have a square base and a volume of 20
ft3. If the material for the base costs
$0.37/ft2, the material for the sides costs
$0.10/ft2, and the material for the top costs
$0.13/ft2, determine the dimensions (in ft) of the box
that can be constructed at minimum cost.

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