Final answer:
Mitochondria produce large quantities of ATP when glucose and oxygen are available to the cell through cellular respiration.
Step-by-step explanation:
The organelle that produces large quantities of ATP when both glucose and oxygen are available to the cell is the mitochondria. Mitochondria are often referred to as the 'powerhouses' or 'energy factories' of the cell because they are responsible for making adenosine triphosphate (ATP), the cell's main energy-carrying molecule. Mitochondria use the energy from organic compounds, such as glucose, to produce ATP through a process called cellular respiration.