Final answer:
The Golgi apparatus in a eukaryotic cell is responsible for producing transport vesicles that are used in exocytosis.
Step-by-step explanation:
In a eukaryotic cell, the organelle that produces transport vesicles for exocytosis is the Golgi apparatus. The Golgi apparatus manipulates products from the Rough Endoplasmic Reticulum (ER) by organizing, modifying, packaging, and tagging them. It then packages these products into transport vesicles. Some of these vesicles transport their contents to other areas of the cell, while others are involved in exocytosis, exporting substances out of the cell. Therefore, the correct answer is A. Golgi Body.