The cellular component that produces proteins by following coded instructions from the nucleus is the ribosome.

Here's a breakdown:

* DNA in the nucleus contains the genetic code, which is a set of instructions for building proteins.

* Transcription: The DNA code is copied into a messenger molecule called messenger RNA (mRNA).

* mRNA travels out of the nucleus and into the cytoplasm, where ribosomes reside.

* Ribosomes: These are complex molecular machines that read the mRNA code and use it to assemble amino acids into a specific protein chain.

* Translation: This process of converting the mRNA code into a protein is called translation.

So, the ribosome is essentially the protein-building factory of the cell, following the instructions provided by the nucleus through mRNA.