The cellular component located within the nucleus that is directly responsible for producing ribosomes is the nucleolus.

Here's why:

* Ribosomes are essential for protein synthesis. They read the genetic code from messenger RNA (mRNA) and translate it into a chain of amino acids, forming proteins.

* The nucleolus is a dense region within the nucleus where ribosomal RNA (rRNA) is transcribed and assembled with proteins to form the ribosomal subunits.

* Ribosomal subunits are then exported from the nucleus to the cytoplasm, where they combine to form functional ribosomes.

So, the nucleolus is the central hub for ribosome production in the cell.