  We prove a large deviation principle and give an expression for the rate
function, for the last passage time in a Bernoulli environment. The model is
exactly solvable and its invariant version satisfies a Burke-type property.
Finally, we compute explicit limiting logarithmic moment generating functions
for both the classical and the invariant models. The shape function of this
model exhibits a flat edge in certain directions, and we also discuss the rate
function and limiting log-moment generating functions in those directions.
