The alternator should run at 14.4 volts without jumpers attached. If it is running at 11.9 like you mention then it is weak. It has probably been weak for a long time. The cars system will take 12V DC to run, so the battery has not been charging for a while, in my opinion. If you leave the car run, it is not going to help. There in not enough voltage from the alternator.
Also on that note, batteries, at least here, typically have a 5 year pro rated warranty. If that battery is stamped dec 2012, you should be able to get somewhere in the neighbourhood of 1/2 back to put towards the purchase of a new one, if you take it to where ever it was bought. The only issue you may run into, with such a badly discharged battery, the may suspect that there was abuse to it(bad alternator, left your lights on for days at a time, multiple time... various other things) and may try and disqualify this from warranty. Typically, the battery will not start your car with less then 10 volts or so.