Question

Minimizing Packaging Costs A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs $0.28/ft2, the material for the sides costs $0.10/ft2, and the material for the top costs $0.22/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. x = ft y = ft.

Answer #1

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 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.

A rectangular box is to have a square base and a volume of 20
ft3. If the material for the base costs $0.17/ft2, the material for
the sides costs $0.06/ft2, and the material for the top costs
$0.13/ft2,
(a) determine the dimensions (in ft) of the box that can be
constructed at minimum cost.
(b) Which theorem did you use to find the answer?

Minimizing Heating and Cooling Costs A building in the shape of
a rectangular box is to have a volume of 6,144 ft3 (see the
figure). It is estimated that the annual heating and cooling costs
will be $2/ft2 for the top, $4/ft2 for the front and back, and
$3/ft2 for the sides. Find the dimensions of the building that will
result in a minimal annual heating and cooling cost. What is the
minimal annual heating and cooling cost? The base...

A rectangular box is to have a square base and a volume of 40
ft^3. If the material for the base costs $0.36/ft^2, the material
for the sides costs $0.05/f^2, and the material for the top costs
$0.14/ft^2, determine the dimensions of the box that can be
constructed at minimum cost.
length____ft
width____ ft
height________ ft

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.

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...

A rectangular box must have a volume of 2 cubic meters. The
material for the base and top costs $ 2 per square meter. The
material for the vertical sides costs $ 8 per square meter. (a)
Express the total cost of the box in terms of the length (l) and
width (w) of the base. C = $ (b) Find the dimensions of the box
that costs least. length = meters width = meters height =
meters

A rectangular box with a square base has a volume of 4 cubic
feet. If x is the side length of the square base, and y is the
height of the box, find the total cost of the box as a function of
one variable The material for the bottom of the box costs $3 per
square foot, the top costs $2 per square foot, and the four sides
cost $5 per square foot. If x is the side length...

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