Trays, tubs and other plastic packaging are invariably made of different plastic polymer types, and those that are made of the same polymer have a different Melt Flow Index (MFI)anyway. This means that the material will not be consistent, which is the absolute key in plastics processing. Some examples: Yoghurt pots can be made from either polypropylene (PP) or polystyrene (PS), and there is no pattern as to which is used where.
If you try to manufacture something from a blend of PP/PS you end up with something of no physical strength that will simply delaminate. Trays could be PP/PS/PVC or others, each of which has radically different melt points and physical properties, so by the time you are melting one polymer in the mix, you could easily be degrading another. More.
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