It is either 32:1 or 40:1, take your pick, with 40:1 being the factory recommendation I believe. 32:1 would be safer, but might reduce performance a bit, and will smoke more. Some 2-strokers think the 32:1 ratio makes them run hotter. There are others that think 40:1 is too lean on oil and will cause engine failure. I do not know, since I have never owned a 2-stroke quad, so take my comments for what they are worth. I do run 32:1 in all my 2-stroke yard and garden engines (tiller, leaf blower, string trimmer). The last 2 are 15+ years old and still running good.
32:1 is 4 oz. of oil to every gallon of gas. Use of a synthetic oil is recommended these days by all 2-strokers I know. In years past some used soybean oil, but it proved less than satisfactory in the long run.
If there is no 2-stroke smoke coming out of the exhaust it is safe to bet the injector is not working. Even if it is working there is a chance it will run with too little oil injected, or the tank will run low and lean out the mix. Most 2-strokers think it is safer to pre-mix, since at low rpms you are getting very little oil from the injector. The injector is engine speed based, so if your quad is run at low speed a lot, definitely pre-mix. There have been cases where a 2-stroke quad was allowed to run at idle for a while (read: too long) and seized up.
Here is a short write up on the LT80 oil, which should apply to your LT50 as well.http://www.weeksmotorcycle.com/lt80_engine_oil.html