Question

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?

Answer #1

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 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 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 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 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 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.

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 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 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

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