# Max and Min Problems

## Homework Statement

The object is to fold and then cut square corners from a standard 8.5 by 11 inch sheet of paper to create a suitcase of maximal volume

V=L*W*H
SA=2LW+2LH+2WH

## The Attempt at a Solution

93.5=2(8.5-2x)(11-2x)+2(11-2x)2x+2(2x)(8.5-2x)
x=1.375

then i plugg it into the Volume equation my lenghts are
(8.5-2(1.375))=5.75
(11-2(1.375))=8.25
1.375=1.375

Then i try to build it out of a piece of paper and it doesn’t close like it is suppose too, can anyone figure out where I went wrong it would be greatly appreciated

LCKurtz
Homework Helper
Gold Member
What does surface area have to do with this problem? And how do you fold and then cut corners out? And how do you fold it to make a suitcase with the corners missing?

Please state the problem, word for word, from your text, along with any pictures they give.

That was word for word. Im not sure if you needed the surface area i was just trying to solve for x since there is only so much paper. So you have a piece of paper an you have to cut the corners out to construct a box with the maximum volume inclosed. So their must be a lid on the box so its like a suitcase.

Mentallic
Homework Helper
It's not closing because you're making an open box from what I can see.

I assume x means the height and this is the type of box you're supposed to be creating (I'm unsure if this design will make for max volume though):

http://img30.imageshack.us/img30/654/boxlayout.png [Broken]

where a=8.5, b=11

So $8.5-2h=w$
and $11-2h=2l$ while it looks like you made it $11-2h=l$

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LCKurtz
Homework Helper
Gold Member
That was word for word. Im not sure if you needed the surface area i was just trying to solve for x since there is only so much paper. So you have a piece of paper an you have to cut the corners out to construct a box with the maximum volume inclosed. So their must be a lid on the box so its like a suitcase.

You can make an open top box by folding up the flaps after cutting square corners out of the paper. I have no idea how to fold it to make a closed container. Are you certain the box is to be closed? You can still calculate the volume a box would hold even if it doesn't have a top.

You can make an open top box by folding up the flaps after cutting square corners out of the paper. I have no idea how to fold it to make a closed container. Are you certain the box is to be closed? You can still calculate the volume a box would hold even if it doesn't have a top.

yea the box must have a top

LCKurtz
Homework Helper
Gold Member
yea the box must have a top

Please supply a picture of how you cut square corners out of a sheet of paper then fold it to make a closed rectangular box. I don't see how you do that and you can't work the problem without knowing how it is folded.

Mentallic
Homework Helper
And is my picture just for decoration?

LCKurtz
Homework Helper
Gold Member
And is my picture just for decoration?

Your picture does not show cutting square corners from the sheet as the OP requires. I can't speak to how decorative it is.

jambaugh
Gold Member
Yea, as I read it, its an open topped box from the fact that the corners cut out must be square. Presumably you will make the lid separately, or travel with all your stuff open to the elements.

Mentallic
Homework Helper
Your picture does not show cutting square corners from the sheet as the OP requires. I can't speak to how decorative it is.

Oh gosh you're right! Actually... *attempts to cover mistake ingeniously*.. I assumed square corners implied rectangles

In that case, I second post #2. How do you do it?