Question

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.)

Answer #1

comment if you need further clarification on this 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 =

A cargo container in the shape of a rectangular box must have a
volume of 480 cubic feet. If the bottom of the container costs $4
per square foot to construct, and the sides and top of the
container cost $3 per square foot to construct, find the dimensions
of the cheapest container which will have a volume of 480 cubic
feet.

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?

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 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 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 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

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.

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 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?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 24 minutes ago

asked 28 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago