Cutting equal numbers of different length pieces from a known length

[jeff_fall2k5]

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!

 

[Rainbow Child]

The number of bars is fixed, or you can have as many as you want?

 

[jeff_fall2k5]

you can have as many 240" bars as you want. Infact, what I really need is 241 sets of the 5 shorter lengths.

 

[Rainbow Child]

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!

 

[jeff_fall2k5]

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