Cutting equal numbers of different length pieces from a known length

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    Cutting Length Numbers
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Discussion Overview

The discussion revolves around the problem of cutting equal numbers of five different lengths of pieces from a known length of material (240 inches) while minimizing scrap material. Participants explore potential mathematical techniques and approaches to optimize the cutting process.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant describes the need to cut equal numbers of pieces of lengths 72.16", 71.64", 68.94", 45.46", and 44.13" from 240" bars while minimizing scrap.
  • Another participant inquires whether the number of bars is fixed or if there can be as many as needed.
  • A participant clarifies that they can have as many 240" bars as necessary and specifies the requirement for 241 sets of the five lengths.
  • One participant acknowledges the constraints of the problem and expresses a willingness to explore how the cuts should be made.
  • A participant seeks advice on applicable mathematical techniques for solving this type of problem, mentioning matrices and the complexity involved.

Areas of Agreement / Disagreement

Participants generally agree on the nature of the problem and the need for optimization, but there is no consensus on specific mathematical methods or solutions to apply.

Contextual Notes

The discussion does not resolve the mathematical techniques applicable to the problem, and participants express uncertainty about the best approach to take.

Who May Find This Useful

Individuals dealing with optimization problems in cutting materials, particularly in manufacturing or production settings, may find this discussion relevant.

jeff_fall2k5
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Hello everyone. I'd like to thank everyone for their help in advance.

Ok, here we go. I've got bars of known length (240"). And, I've got to cut equal numbers of 5 different length pieces. The lengths are: 72.16", 71.64", 68.94", 45.46", and 44.13" The whole point is to minimize the amount of scrap material.

I'm going ahead with a more or less trial and error approach. This isn't really working too well. I'd like to somehow know that I've found the best method for making the cuts. I have to think that this is such a common problem that it's been figured out. Anyway, I'm not familiar with any mathematical techniques that are well suited for solving this problem.

Thanks!
 
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The number of bars is fixed, or you can have as many as you want?
 
you can have as many 240" bars as you want. Infact, what I really need is 241 sets of the 5 shorter lengths.
 
Aha! You do have a constraint!
Ok! I will try to find out how the cuts must be done. I don't know how right now, but I will try! :smile:
 
Thanks a lot! You know, I'm going to have very similar type problems for prolly the rest of my career. Is there any type of math that can be applied to this problem? I mean, matrices sure come in handy at times, but there's really a lot more to it
 

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