Question

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

Answer #1

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.

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 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?

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 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 box with square base and open top is to have a volume of 10?3
. Material for the base costs $10 per square meter and material for
the sides costs $8 per square meter. Determine the dimensions of
the cheapest such container. Use the first or second derivative
test to verify that your answer is a minimum.

rectangular tank with a square base, an open top, and a volume
of 8788 ft^3 is to be constructed of sheet steel. Find the
dimensions of the tank that has the minimum surface area.

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 storage container with an open
top and a square base is to be
constructed. Material for the bottom costs $6/sq-ft, and material
for the sides costs $3/sq-ft.
If a total of $72 is budgeted for material expenses, what are
the dimensions of the container that holds the largest volume?

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