Question

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 =

Answer #1

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.

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.

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?

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.

A closed rectangular box is to contain 12 ft^3 . The top and
bottom cost $3 per square foot while the sides cost $2 per square
foot. Find the dimensions of the box that will minimize the total
cost.

You have been asked to design a closed rectangular box that
holds a volume of 25 cubic centimeters while minimizing the cost of
materials, given that the material used for the top and bottom of
the box cost 4 cents per square centimeter, and the material used
for sides cost 9 cents per square centimeter. Find the dimensions
of this box in terms of variables L, W, and H.

Suppose you want to build a hollow rectangular box with volume
2000 cm^3. If the material for the top costs $3/cm^2 and the
material for the side and bottom faces cost $1/cm^2, what are the
dimensions of the cheapest box? (Here, we ignore the thickness of
the faces of the box.)

The volume of a square-based rectangular box is 252 dm^3. The
construction cost of the bottom is $5.00 per dm^2. of the top is
$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 company plans to manufacture a rectangular box with a square
base, an open top, and a volume of 404 cm3. The cost of the
material for the base is 0.5 cents per square centimeter, and the
cost of the material for the sides is 0.1 cents per square
centimeter. Determine the dimensions of the box that will minimize
the cost of manufacturing it. What is the minimum cost?

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