An open-top rectangular box has a volume of 250 cm 3. The width
of the box...
An open-top rectangular box has a volume of 250 cm 3. The width
of the box is 5 cm. The cost is $2/ cm 2 for the base and $1/ cm 2
for the other sides. What is the minimum cost for making the
box?
A rectangular box with a square base and an open top and a
volume of 1ft^3 is to be made. Suppose the material used to build
the sides cost $4 per ft^2 and the material used to build the
bottom costs $1 per ft^2. Determine the dimensions (i.e. the
side-length of the base and the height) of the box that will
minimize the cost to build the box.
Note: if we let x denote the side-length of the base and...
A box with a square base and open top must have a volume of
32000 cm^3. Find the dimension of the box that minimize the amount
of material used. (show all work)
An open-top rectangular box is being constructed to hold a
volume of 400 in3. The base of the box is made from a
material costing 7 cents/in2. The front of the box must
be decorated, and will cost 10 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:
Depth:
Height:
A company plans to design an open top rectangular box with
square base having volume 4 cubic inches. Find the dimension of the
box so that the amount of materiel required for construction is
minimal.
(a) Find the dimension of the box so that the amount of materiel
required for construction is minimized.
(b) What is the minimized material required for the
construction?
A box with an open top is to be constructed out of a rectangular
piece of cardboard with dimensions length=10 ft and width=11 ft by
cutting a square piece out of each corner and turning the sides up.
Determine the length x of each side of the square that
should be cut which would maximize the volume of the box.
A rectangular box with no top is to be made to hold a volume of
32 cubic inches. Which of following is the least amount of material
used in its construction?
a.) 80 in2
b.) 48 in2
c.) 64 in2
d.) 96 in2
We want to design a rectangular box without a lid with a volume
of 64000 cm^3. Find the dimensions that maximize the surface area.
Using Lagrange Multipliers
Can you explain your reasoning pls
An open-top rectangular box is to be constructed with 300 in2 of
material. If the bottom of the box forms a square, what is the
largest possible box, in terms of volume, that can be
constructed?
An open cardboard box (with no top) is to be constructed so that the width of the box is four times its length. The length of the box is labeled x in the picture. You have 100 in2 of cardboard to use. Find the length x and the height y that maximize the volume of the box. (a.) Find a formula for the volume V in terms of x and y. (b) Use the constraint given by the amount of cardboard available...
A rectangular storage container with an open top is to have a
volume of 16 cubic meters. The length of its base is twice the
width. Material for the base costs 15 dollars per square meter.
Material for the sides costs 6 dollars per square meter. Find the
cost of materials for the cheapest such container.