Question

box with rectangular base to be constucted

material cost $4 /in^2 for the side & $5/in^2 for top and bottom.

if box is to have 90in^3 and the length of its base is 2X width, what are dimensions of box that would minimize cost of construction?

Answer #1

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. 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.
(a) 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.
(b) Find the critical number...

A rectangular box with capacity 355cc is to be produced. The
bottom and side of the container are to be made of material that
costs 0.02 cents per cm^2, while the top of the container is made
of material costing 0.03 cents per cm^2. Set up to find the
dimensions that will minimize the cost of the container.
a.) Cost of top =
b.) Cost of bottom =
c.) Cost of side material =
d.) Total Cost of materials =

The volume of a square-based rectangular box is 252 dm^3. The
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$2.00 per dm^2 and of the sides is $3.00 per dm^2. Find the
dimensions that will minimize the cost if the side of the base must
fall between 4 dm and 8 dm.

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...

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 square base has a volume of 4 cubic
feet. 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 Find the critical number of the cost function.

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.

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
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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
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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...

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