Question

3. A large box is made from a piece of cardboard that measures 10ft by 10ft . Squares of equal size (side length x) will be cut out of each corner. The sides will then be folded up to form a rectangular box.

a) Write down a formula for V(x), the volume of the cardboard box.

b) What are the critical values for V(x)?

c) What size square should be cut from each corner to obtain maximum volume?

d) What is that maximum volume?

4. Weyland-Yutani has started to get into the smartphone business. Currently there is a uniform annual demand for 9000 W-Y phones. It costs $5 to store a single smartphone for an entire year. And it costs $2500 to set up the assembly line to manufacture a run of phones. Let x = the number of phones made in each run.

a) How many runs are carried out each year (in terms of x)?

b) What is the formula for C(x), the total annual costs associated with storage and setting up the line?

c) Find the value of x which minimizes C(x).

d) Write the minimum value of C(x).

show work please

Answer #1

A rectangular box is made from a piece of cardboard that
measures 48cm by 18cm by cutting equal squares from each corner and
turning up the sides. Find the maximum volume of such a box if:
a) The height of the box must be at most 3cm.
b) The length and width of the base must at least 10cm.

An open box is to be made from a 16-inch by 30-inch piece of
cardboard by cutting out squares of equal size from the four
corners and bending up the sides. What size should the squares be
to obtain a box with the largest volume?
a. Draw and label the diagram that shows length x and width y of
the box.
b. Find the volume formula in terms of x.
c. Find the x value for which the rectangle has...

From a thin piece of cardboard 40in by 40in., square corners are
cut out so that the sides can be folded up to make a box. What
dimensions will yield a box of maximum volume? What is the maximum
volume? Round to the nearest tenth if necessary.

A piece of cardboard measuring 11 inches by 10 inches is formed
into an open-top box by cutting squares with side length x from
each corner and folding up the sides. Find a formula for the volume
of the box in terms of x V ( x ) = (11-2x)(10-2x)(x)
Find the value for x that will maximize the volume of the box x
=

Rectangular box is made from a piece of cardboard that is 24
inches long
and 9 inches wide by cutting out identical squares from the four
corners and turning up
the sides. Find the dimensions of the box of maximum volume. What
is this maximum
volume?

An open box is to be made from a 2-meters by 6-meters piece of
cardboard by cutting out squares of equal size from the four
corners and bending up the sides. Find the dimensions of the box
that would give the largest volume? Justify your answer by
displaying all work. Make sure to display the proper formulas for
the length and width in terms of x.

A company must build a cardboard box (without a lid) from a recycled cardboard sheet of
21x21cm. Determine the dimensions of the box so that its volume has maximum capacity.
Use the optimization method to determine the measure of the cuts.
a). The cut at each corner must be = ___ cm
b) The box's volume is = ___ cubic cm

From a thin piece of cardboard 60 in. by 60 in. square corners
are cut out so that the sides can be folded
up to make a box. a) What dimensions will yield the maximum volume?
b) What is the maximum
volume?
Please answer all parts, show all steps and explanations. I have
the solution I don't know how to get there. Thank you.

A piece of cardboard is twice as long as it is wide. It is to be
made into a box with an open top by cutting 2 cm squares from each
corner and folding up the sides. Let x represent the width of the
original piece of cardboard. Find the width of the original piece
of cardboard,x, if the volume of the box is 1120 cm^3

A box with an open top is made from a square sheet of cardboard
with an area of 10,000 square in. by cutting out squares from the
corners and folding up the edges. Find the maximum volume of a box
made this way. (draw a picture).

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