If you only operate ONE at a time, you should not overload the circuit. If you absolutely need a new circuit, I would plan on several hundred dollars. New circuit breaker GFCI type, new cable run from garage to lanai location, new box, outlets and cover, and several hours of work. I would also have the new circuit go to the soffit areas this should simplify the routing of the wires from the lanai blinds to the new outlet, and the wiring to the outlet will be simplified. You will be able to route the wiring behinds the soffit.
I would get at least 3 bids for the work.
__________________
Pennsylvania, for 60+ years, most recently, Allentown, now TV. 
|