I mainly agree with @Arthur-Bomber-Harris, but my suggestion would be that before you build a Middle East factory that you bring the South Africa factory fully online. That factory can produced mechanized infantry, fighters, and infantry (with transports to move them) that call all assist in the Middle East. If your sole sources of defensive units for the Middle East are Egypt and a Middle East factory, your output will be overwhelmed more quickly than if you also utilize a South Africa factory. The reason I would use the South Africa factory first is because it takes longer for units to reach the battlefront.
Your local Middle East factories can produce critical but slow-moving infantry units, while your Egypt and South Africa factories can produce fast movers that can reach the Middle East more quickly than infantry.
Once the Middle East falls (and it will unless the UK and US are able to pressure Europe heavily), that South Africa factory makes Egypt viable for longer as well. Troops in the pipeline from South Africa to the Middle East naturally move through Egypt.
Marsh