Math Is Fun Forum

Uni

Member

Registered: 2021-05-20

Posts: 1

Number of Cuts

Hi all, I am working on a math question that is causing me headache. I have a number of materials (length and number are known) and the sections (length and numbers are known) cut from the original materials. I have to determine the POSSIBLE numbers of cuts produced based on the data I have. Here are the sets of numbers:

Original materials (L=length) (there are few lengths that are repeated due to the different types of the original materials, but I have no info on the types of cut sections produced):
12mL x 32nos; 6mL x 56nos;
10mL x 51nos; 11mL x 50nos;
12mL x 48nos; 4.5mL x 97nos;
6mL x 180nos; 6.8mL x 2nos;
7mL x 3nos; 7.2mL x 7nos;
7.5mL x 3nos; 8mL x 2nos;
9mL x 30nos; 10mL x 49nos;
11mL x 16nos; 12mL x 366nos;
9mL x 10nos; 12mL x 182nos

Cut sections produced:
3.5mL x 489nos; 3.1mL x 8nos;
3mL x 527nos; 3.2mL x 2nos;
4.9mL x 1nos; 5mL x 138nos;
4.2mL x 1nos; 3.4mL x 2nos;
4.5mL x 851nos; 4mL x 504nos;
3.3mL x 4nos; 2.5mL x 8nos;
2mL x 2nos; 2.9mL x 1nos;
3.8mL x 6nos; 2.8mL x 5nos;
4.4mL x 1nos; 3.75mL x 19nos;
2.75mL x 17nos; 4.75mL x 12nos;
3.25mL x 20nos; 6mL x 46nos;
6.5mL x 15nos; 5.5mL x 12nos;
7mL x 5nos

Appreciate any help. Thanks.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Number of Cuts

hi Uni

Welcome to the forum.

I'm trying to get my head around this situation and exactly what you are asking.

This is what it looks like to me.  If I've got it totally wrong, please give more details.

Original lengths are like this:

32 lengths each 12metres long.
56 lengths each  6 metres long
................................. 16 more lines of information like this.........................

Then you want to cut up the lengths to produce:

489 lengths each 3.5 metres long.
8 lengths each 3.1 metres long.
and so on.

You want to know (1) Can this be done at all?  (2) What's the best cutting plan?

I haven't yet checked if the total length available is sufficient for the total length after cutting.  Obviously if it isn't then the problem cannot be satisfactorily answered.  If there's some left over, does it matter what's left; are you hoping to maximise the left over lengths?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob