The structures of a cell that work together to produce ATP energy needed for cell processes are the cell membrane and mitochondria.
The mitochondria are known as the "powerhouses" of the cell, where ATP is produced through cellular respiration. The cell membrane plays a role in transporting nutrients and oxygen needed for this process, as well as in the release of ATP to various parts of the cell.
So, the correct answer is:
cell membrane and mitochondria.