Firstly, I agree with the other posters that the original question is poorly worded and ambiguous.
The debate that has led on from it has shown some confusion, both about take-off optimisation and about the effect of V1 on take-off performance.
Effect of V1
The term "field length limited" covers 5 basic performance scenarios:
1) You are limited by take-off run, all engines operating.
2) You are limited by take-off run, one engine inoperative.
3) You are limited by take-off distance, all engines operating.
4) You are limited by take-off distance, one engine inoperative.
5) You are limited by accelerate-stop distance.
So, if we change V1 but keep all other factors the same (this includes weight), we can have a variety of effects:
a) By definition, V1 has no effect on the all engines operating cases (1&3).
b) If V1 is increased, the accelerate-stop distance required will increase. This is intuitive, as we must assume that the aircraft will stop from a higher speed than before.
c) The take-off run and distance required, with one engine inoperative will decrease. This is not as clear as point b, but remember that we said that all other factors will stay the same. So, we will still have to reach the same Vr for rotation. The higher V1 means we can assume that the point of engine failure (Vef) happens later and the aircraft spends more off the take-off run with both engines operating, thereby accelerating faster and using less distance.
So, the effect of a change in V1 on a field length limited take-off depends upon which of the factors is actually limiting!