What's the most cost effective way to handle this dead battery?

Here's the story: 79 Trans Am is rarely driven. I have been starting it and driving it for 20 minutes once every 2 weeks. The battery is only a year old. Eventually I had to jump start the car. Now I can't even jump it like I used to. I used to connect the cables, start the other car and the Trans Am... show more Here's the story:
79 Trans Am is rarely driven. I have been starting it and driving it for 20 minutes once every 2 weeks. The battery is only a year old. Eventually I had to jump start the car. Now I can't even jump it like I used to. I used to connect the cables, start the other car and the Trans Am would start right up. The other day I ran the other car (a 6 cylinder) for 20 minutes and got nothing. I wouldn't mind running it for longer if I thought I was going to get anywhere. (If it matters, the car's clock is still running). Additonally AAA came out the last time this happened and said the battery was a goner. I took their word for it and replace the battery. Now it's happening again and I just want to make sure I'm making the most sensible choice. I'm reading about people who connect their battery to some sort of gizmo for a day or two and that does the trick. Any advice? Should I get this gizmo? How much do they cost? Or should I just run this other car for longer? How can I tell for myself if a battery is really completely dead? Also, does it do any good to rev the engine of the running vehicle? Lots of questions I know. Thanks in advance for your help.
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