Blood work results: WBC and RBC levels?

Hopefully I landed in the right subforum. If not, my bad—mods, please feel free to move this where it belongs.

Hey everyone. I was wondering if someone could explain how red or white blood cells (leukocytes/platelets) are actually obtained or produced. From what I understand, they come from bone marrow... but can they be manufactured synthetically in a lab? When you see a doctor, they can just administer a dose of cells if you're short on them, so I'm curious where that supply comes from. It's not like they're just pulling it out of thin air from some other person's blood, right?

Thanks for any insight... 🙂