The two organelles that work together to produce new membranes for the cell are the rough ER (endoplasmic reticulum) and mitochondria.
The rough ER is involved in synthesizing proteins that are typically incorporated into membranes or secreted from the cell, while mitochondria produce ATP, which provides energy necessary for various cellular processes, including membrane synthesis. However, if you are looking for more specific partners in membrane production, the rough ER is generally associated with this function directly due to its ribosomes synthesizing membrane proteins.
If you're choosing strictly from the options provided, the best answer that relates to new membrane production is rough ER (endoplasmic reticulum), with mitochondria supporting cellular energy needs.