The ribosomes are produced in:

• The largest structure in the eukaryotic cell's nucleus is nucleolus where it primarily serves as the site of ribosome synthesis and assembly.
• Nucleoli also have other important functions like the assembly of signal recognition particles and playing a role in the cell's response to stress.
• On the basis of the ribosomes endoplasmic reticulum can be classified as rough endoplasmic reticulum and smooth endoplasmic reticulum.
• Endoplasmic reticulum with ribosomes is called rough endoplasmic reticulum
• ER without ribosomes is refer as smooth endoplasmic reticulum.

Hence, option A is the correct answer.