Math Is Fun Forum

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.