Question

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,

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 20
ft3. If the material for the base costs
$0.37/ft2, the material for the sides costs
$0.10/ft2, and the material for the top costs
$0.13/ft2, determine the dimensions (in ft) of the box
that can be constructed at minimum cost.

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.

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 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.

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
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. x...

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 20
ft3. If the material for the base costs $0.17/ft2, the material for
the sides costs $0.06/ft2, and the material for the top costs
$0.13/ft2,
(a) determine the dimensions (in ft) of the box that can be
constructed at minimum cost.
(b) Which theorem did you use to find the answer?

A large shipping crate is to be constructed in a form of a
rectangular box with a square base. It is to have a volume of 441
cubic feet. The material for the base of the crate is steel that
costs $6 per square foot, the rest of the crate is constructed out
of wood. The wood for the top of the crate is less expensive at $3
per square foot and the sides will be constructed from the wood...

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