# Max and Min Problems

1. Jan 18, 2010

### Punkyc7

1. The problem statement, all variables and given/known data
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

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

3. 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

2. Jan 18, 2010

### LCKurtz

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.

3. Jan 18, 2010

### Punkyc7

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.

4. Jan 18, 2010

### Mentallic

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 $11-2h=l$

Last edited by a moderator: May 4, 2017
5. Jan 18, 2010

### LCKurtz

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.

6. Jan 18, 2010

### Punkyc7

yea the box must have a top

7. Jan 18, 2010

### LCKurtz

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.

8. Jan 18, 2010

### Mentallic

And is my picture just for decoration?

9. Jan 19, 2010

### LCKurtz

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

10. Jan 19, 2010

### jambaugh

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.

11. Jan 20, 2010

### Mentallic

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?

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