The questions are always worth asking !
The short answer is most 'can I feed them cheaper' questions is 'not to any significant degree'
If you can get free stuff, then you can make a difference, but all free stuff will not be in the right nutritional proportions, so they will take longer.
The simple logic is that if you can take x + y + z and make it a cheaper feed than a large industrial company with economies of scale, vast buying power etc. - then why are they not doing that?
So yes home mixed feeds can look cheaper, but they will lack key amino acids that let the pig build muscle and much of the additional protein is simply pooed out as it is not in the correct ratios, so they either take longer to fatten (so more feed and benefit is lost) or run to fat, or both !