A useless & somewhat insane hypothetical

[ilya]

Say it's folded to you on the button and you have JJ. There is no SB in this hand, so it's just you and the BB. You both have XXxbb and you somehow KNOW 3 things:

1, he has 66
2, he will call any amount preflop
3, he will SOMETIMES fold to a bet on the flop (depending on pot size) but will always check/call with a set or better.

You also plan to push the flop no matter what.

What's the optimal amount to bet preflop in a tournament?