need skematik, cost-effective design for building crates

[louie]

I need to make 10 crates out of plywood to ship neon lights. I have made some in the past for the same purpus. My question is as fallows. I would like to know that if I gave you the sizes of thees boxes could you tell me how many sheets of 4x8 plywood I would need? I am looking for the most efficient way to cut thees sheets. it is of the utmost importance for cost effectiveness. I'm also looking for a skematik if at all possible. It would be greatly appreciated if you can assist me in this endeavor. Thank you in advance for your cooperation. My contact is .... {Personal email deleted} Thanks Louie

 

[morson]

Describe the crates. Are they cubic, cuboids? Are they open at the top? Describe also what you mean by "size." Do you mean the volume, or the dimensions?

I'm assuming your boxes will have a variable length l, width w, and height h. I'm assuming the volume is fixed (as in, you know the volume and will tell us), so it is a constant V. I am assuming they are cuboids. I am also assuming the boxes have plywood covering all bases (no open ends). These are heavy assumptions, but you haven't been very informative.

The surace area of the box is therefore \(\displaystyle 2(\frac{V}{l} + hl + \frac{V}{h})\), so you'd probably need \(\displaystyle \frac{(\frac{V}{l} + hl + \frac{V}{h})}{16}\\) of those 4x8 sheets for one crate, so you'd need \(\displaystyle 5\frac{(\frac{V}{l} + hl + \frac{V}{h})}{8}\\) 4x8 sheets overall. Perhaps if you wrote back with some more specifications and the size of the boxes in question, determining the height and width variables in terms of the fixed volume would help me to give you a numerical suggestion for how many sheets you need.

 

[tkhunny]

Of corse, morson's suggestions cover only the minimum bound. There is in that formulation no room for kerf, waste in general, fastening edges reliably, reinforcing, or expanding for insulation and padding during shipment. There may be other considerations. These are only those that came immediately to mind.

 

[stapel]

I need to make 10 crates out of plywood to ship neon lights....it is of the utmost importance for cost effectiveness. I'm also looking for a skematik if at all possible.

Note: This is a math tutoring forum. Math volunteers tutor math students with math questions from their math homework. Not many (or any?) of us are carpenters, contractors, buyers, architects, or engineers. We do math help, not construction purchasing and design.

For the consulting service you seek, you might want to consider contracting with an appropriate consulting company.

My best wishes to you.

Eliz.

 

[louie]

Of corse, morson's suggestions cover only the minimum bound. There is in that formulation no room for kerf, waste in general, fastening edges reliably, reinforcing, or expanding for insulation and padding during shipment. There may be other considerations. These are only those that came immediately to mind.

Thank you for your concern. I must have failed to mention that I have built these crates before.

You are correct in manner that I have not given the specifics concerning the the saw blade which will consume 1/8 of an inch each time it passes (Kerf). As for the rigidity and construction, I have used 1x2 furring strips which will include wood glue. These strips will also be fashioned with pneumatic nailing brads.

If you are up for the challenge I will be happy to give you the dimensions. Thanks for your reply.

 

[louie]

Note: This is a math tutoring forum. Math volunteers tutor math students with math questions from their math homework. Not many (or any?) of us are carpenters, contractors, buyers, architects, or engineers. We do math help, not construction purchasing and design.

For the consulting service you seek, you might want to consider contracting with an appropriate consulting company.

Thank you for your concern I have looked in other areas and was just passing through this site. I thought that some one would be-up for this math problem. I consider this to be a real world problem that students could benefit from. Not the regular textbook jargon that every one is use to. Thanks again for your help. Yours LOUIE

 

[louie]

Describe the crates. Are they cubic, cuboids? Are they open at the top? Describe also what you mean by "size." Do you mean the volume, or the dimensions?

I will be happy to give you the specifics if you are truly interested in this real world math problem. Thanks for your support LOUIE

 

[stapel]

I thought that some one would be-up for this math problem.

Just because a topic might involve some mathematics does not mean that any random math teacher will have the necessary background for developing a solution. Mathematics is used in many areas of study, almost all of which require years of additional study of and exeperience in other areas, study and experience that almost all math tutors would never have encountered.

I apologize for the confusion.

I consider this to be a real world problem that students could benefit from.

My apologies! I had thought you were posting this to be provided with an architectural design or construction schematic. How silly of me! According to the above, you meant this as a learning exercise for students. That's very kind of you (though naturally confusing for the tutors).

In the interest of benefitting any students who might read this thread (improbable, but possible), please post your complete worked solution.

Thank you!

Eliz.

 

[louie]

Here are the required specifications if any one is up for this challenge. 10 boxes are to be made all of the boxes sides are the same depth. Depth = 7 3/4 inches. All sizes are in inches. Box 30x22 Box 27x21 Box 27x22 Box 27x16 Box 27x21 Box 27x16 Box 32x18 Box 30x18 Box 46x32 Box 58x20 I will be using 4x8 sheet goods 48x96 inches Thank you if any one is willing to take to assist me.

 

[stapel]

Here are the required specifications if any one is up for this challenge....

So this isn't an example of a "real life" use of mathematics that you were posting to be of benefit to students...? You really are expecting math tutors to do free architectural consulting work for you...? :shock:

If so, please see my first reply, wherein it was explained that this is a math-tutoring forum, not a consultancy company. I realize that you are trying to cut costs, but you really do need to hire a trained professional to obtain the professional design schematics you seek.

Thank you for your consideration.

Eliz.

 

[tkhunny]

1) It's too difficult to communicate your precise needs. For example, you still have not indicated whether your measurements are inside or outside lengths. You also haven't suggested the joint design. That will make a significant differrence. This deficiency remains after maybe 2½ tries at a description.

2) Liability. If I answer you incorrectly and you sue me, that will not make me happy. That's why you hire consultants who make promises and sign contracts.

 

[Denis]

Edit: For your 10 boxes, you need these 60 pieces:

4: 7.5 by 16
4: 7.5 by 18
2: 7.5 by 20
4: 7.5 by 21
4: 7.5 by 22
10: 7.5 by 27
4: 7.5 by 30
4: 7.5 by 32
2: 7.5 by 46
2: 7.5 by 58
4: 16 by 27
2: 18 by 30
2: 18 by 32
2: 20 by 58
4: 21 by 27
2: 22 by 27
2: 22 by 30
2: 32 by 46

Adds up to 60: 10 boxes each with 6 sides.

IF you REALLY intended this to be something "interesting"
as a problem for students, then there's no need to introduce
boxes and the likes: only confuses the issue.
Question could be something like:
Required are the following 60 pieces:
(list above)
These 60 pieces are to be cut from 48 by 96 rectangles.
No sticking together allowed; assume no wastage from cutting.
What is the minimum number of rectangles required?

Roger, over and out.

 

[JakeD]

Edit: For your 10 boxes, you need these 60 pieces:

4: 7.5 by 16
4: 7.5 by 18
2: 7.5 by 20
4: 7.5 by 21
4: 7.5 by 22
10: 7.5 by 27
4: 7.5 by 30
4: 7.5 by 32
2: 7.5 by 46
2: 7.5 by 58
4: 16 by 27
2: 18 by 30
2: 18 by 32
2: 20 by 58
4: 21 by 27
2: 22 by 27
2: 22 by 30
2: 32 by 46

Adds up to 60: 10 boxes each with 6 sides.

IF you REALLY intended this to be something "interesting"
as a problem for students, then there's no need to introduce
boxes and the likes: only confuses the issue.
Question could be something like:
Required are the following 60 pieces:
(list above)
These 60 pieces are to be cut from 48 by 96 rectangles.
No sticking together allowed; assume no wastage from cutting.
What is the minimum number of rectangles required?

Roger, over and out.

Nice description of the problem, Denis!

Knowing this to be a common problem I did this search

http://www.google.com/search?q=minimum+waste+cut+linear+program

and found this program on the first hit.

PS: I think this problem is appropriate for a math help forum.