Ok so i made a mistake on this problem. Turns out this was accidentally a trick question. The answer is that any amount of fuel will get you to any height. The reason being that as the fuel is expended the mass of the ship approaches 0, so acceleration approaches infinity. So by the time the rocket is out of fuel it would be moving at the speed of light no matter how much fuel it started with.
As suck I will post a new version of this question and ill make sure i solve it BEFORE I post it.