Question

You need a box with a volume of 1000cm^{3}. The top and
the bottom of the box are square and each cost $.20 per square
centimeter, whereas the sides each cost $.05 per square centimeter.
What are the dimensions of the box that will minimize the cost?

Answer #1

A box of volume 36 m3 with square bottom and no top
is constructed out of two different materials. The cost of the
bottom is $40/m2 and the cost of the sides is
$30/m2 . Find the dimensions of the box that minimize
total cost. (Let s denote the length of the side of the
square bottom of the box and h denote the height of the
box.)
(s, h) =

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?

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.

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.

Suppose the material for the top and bottom costs b cents per
square centimeter and the material for the sides costs 0.1 cents
per square centimeter. You want to make a can with a volume of k.
What values for the height and radius will minimize the cost? (Your
answer will have a k and a b in it.)

A closed rectangular box is going to be built in such a way that its volume corresponds to 6m3. The cost of the material for the top and bottom is $ 20 per square meter. The cost for the sides is $ 10 per square meter. What are the dimensions of the box that produce a minimum cost?

A box is contructed out of two different types of metal. The
metal for the top and bottom, which are both square, costs $2 per
square foot and the metal for the sides costs $2 per square foot.
Find the dimensions that minimize cost if the box has a volume of
25 cubic feet. Length of base x= Height of side z=?

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 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.

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