Question

A box with a square base and closed top must have a total
surface area of 600 *c**m**2*. Find the
dimensions of the box that maximize its volume (clearly identify
the decision variables, the constraints, and the objective
function. You have to prove that the dimensions you get in the end
are truly the dimensions for the maximum volume, and not the
minimum or anything else)

Answer #1

A closed box with a square base is to have a volume of
2000in2. The material for the top and bottom of the box
is to cost $6 per in2, and the material for the sides is
to cost $3 per in2. If the cost of the material is to be
the least, find the dimensions of the box. Prove/justify
your answer.

A closed rectangular box is to be constructed with a base that
is twice as long as it is wide. If the total surface area must be
27 square feet, find the dimensions that will maximize the
volume.

A box with a square base and open top must have a volume of
108000 cm^3. We wish to find the dimensions of the box that
minimize the amount of material used.
First, find a formula for the surface area of the box in terms of
only x, the length of one side of the square base.
[Hint: use the volume formula to express the height of the box in
terms of x.]
Simplify your formula as much as possible....

A box with a square base and open top must have a volume of
157216 cm3cm3. We wish to find the dimensions of the box that
minimize the amount of material used.
First, find a formula for the surface area of the box in terms of
only xx, the length of one side of the square base.
[Hint: use the volume formula to express the height of the box in
terms of xx.]
Simplify your formula as much as possible....

A box with a square base and an open top must have a volume of
864 cm^3. Find the dimensions of the box that minimize the amount
of material used.

A box with a square base and open top must have a volume of
364500 cm3cm3. We wish to find the dimensions of the box that
minimize the amount of material used.
First, find a formula for the surface area of the box in terms of
only xx, the length of one side of the square base.
[Hint: use the volume formula to express the height of the box in
terms of xx.]
Simplify your formula as much as possible....

A manufacturer sends you 100m2 of material to construct a box
(single layer, closed top). The box must have a square base and be
of maximum volume. Let sbe side length the base of the box, and
hthe height of the box. a) Write an equation for the surface area
covered by the material. b) Determine a formula for the volume V as
a function of the side of s only. c) Determine the dimensions such
that of the 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.

A box with a square base and open top must have a volume of
202612 cm3. We wish to find the dimensions of the box that minimize
the amount of material used.
(Round your answer to the nearest tenthousandths if
necessary.)
Length =
Width =
Height =

A box with a square base and open top must have a volume of
296352 cm3. We wish to find the dimensions of the box that minimize
the amount of material used.
(Round your answer to the nearest tenthousandths if
necessary.)
Length =
Width =
Height =

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