In 2008 after 97,000 miles, a quart of oil was being consumed every 3000 miles; now a year later oil consumption is 1 quart every 1200 miles

You should still be covered under GM powertrain warranty.

Though I am not familiar with the 2007 model, on the e46s, I know that the low oil light comes on when you are down only about 1/2 quart. Does your model have a dip stick?
A half quart in 3000 miles is not cause for concern. Most of them burn a bit less than that, at least during the first 200k miles, but some burn more. It depends to some extent what kind of oil you are using. It will burn more Mobile1 than it will Castrol Syntec, for example.
I have an '04 330 that uses about a half quart in 7k miles between oil changes, and an '04 325 that goes through a quart every thousand miles. I am only a little concerned about the 325. I would not be at all concerned about a half quart in 3k miles.

its used how much ?? thats 8 pints of oil which is about 5 litres in 3000 miles whats it doing leaving a blue haze behind it ,i think this engine needs looking at as this amount of oil consumption will kill the catalytic converter

Oil consumed between oil changes (assuming 2,500 miles) should be between 0 and 1 quart, for a healthy engine.
More oil consumption is annoying, but not viewed as an issue by manufacturers, in fact most would not do anything until you exceeded a quart in 600 miles (I would be livid!!!), but that is how they think of it.

All that being so, the cost of repair far outweighs the cost of the oil, so to rebuild for oil consumption is often not cost effective. Personally, I would go mental at more that a quart between oil changes.

My 1993 voyager is like that. It may burn some , it definitely leaks some , and it could be just sending some through the PCV valve. Oil leaks and burning oil causes pollution . If you can fix it with a new seal or a valve cover gasket it is easier than constantly checking your oil. Temperature, trailering, speed, outdoor temperature, and engine RPM all can be factors if you are losing oil. If your engine is a quart down, the engine oil consumption rate doubles or triples. In other words the lower the oil level the faster it disappears. High mile cars will drive for years as long as you add oil when it is needed (keep the oil level between the marks). Fix any obvious leaks. Then determine your oil change interval (3000 miles, 4000 miles, 5000 miles). I change between 4000 and 5000 miles. If i am a quart low at 3500 I add a quart. If I am a quart low at 4500 miles I just change the oil in the car. A good practice is to carry a quart of oil in your vehicle just in case you need it. It is far cheaper to add a quart when needed than to go to the dealer once to maybe fix a problem that they may not be able to find or fix. Older engines (even some newer ones) just use oil , especially in hotter climates. Fix the obvious and carry a quart.

No more than 1 quart between oil changes ... usually about 3000 miles under most circumstances.

I see you have a four cylinder since it only holds 4.5 quarts.
2006 manual confirms your oil consumption is within allowances. Just check oil every time you buy gas like the manual reccomends. Do not over rev engine or accelerate from stops at max capacity of car as these can increase oil consumption.

JR

you may want to upgrade your oil to a thicker oil that helps alot more than people think its normal anywhere from 1qt to 1/2 a qt every 3000 miles that sounds pretty good and a healthy engine upgrade on brands and viscosity that should take care of that but it will burn more oil if the engine is being broken into for the first time if its brand new

That's within acceptable limits according to Hyundai Motor America's standard: For a proper diagnosis, the amount of oil consumed over a known mileage should be checked three times and then averaged.The accumulated mileage divided by the total amount of oil added will give the consumption rate in miles per quart. If the oil consumption rate is greater than 1 quart per each 1000 miles, further diagnosis may be required.

I do not believe there is a fix by Chrysler. My van has 50000 and seems oil consumption is getting worse. It is either past the valve seals or the piston oil control ring. I believe Chrysler KNOWS ALL ABOUT THIS! If you google search this there are to many complaints! 1 quart every 3 thousand miles is not exceptable unless you are driving a model T!