Which part of the cell is responsible for the production of ribosomes?

The nucleus is indeed responsible for the production of ribosomes. Inside the nucleus, a specific region called the nucleolus plays a crucial role in ribosome biogenesis. It is where ribosomal RNA (rRNA) is synthesized and combined with ribosomal proteins to form the subunits of ribosomes. Once these subunits are assembled, they are exported from the nucleus into the cytoplasm, where they combine to form functional ribosomes that are critical for protein synthesis in the cell.

In contrast, the rough endoplasmic reticulum (RER) does not produce ribosomes; instead, it is studded with ribosomes on its surface and is involved in the synthesis and processing of proteins that will either be secreted from the cell or inserted into membranes. The Golgi apparatus primarily functions in modifying, sorting, and packaging proteins and lipids that have been synthesized in the endoplasmic reticulum, rather than producing ribosomes. The plasma membrane surrounds the cell and regulates the movement of substances in and out of the cell, having no direct role in ribosome production. Thus, the nucleus is the correct answer as it is the site where ribosomes are actually produced.