Let's say left door lies and right door tells the truth. Right door leads out.
Left door would lie and say "right door would tell you I am the door that leads out"
Right door would tell the truth, and say "left door would say LEFT door leads to freedom". Since left door does not lead to freedom, left door would lie and say that left door is the correct one.
No matter which door you ask, they will have the same answer.
So you would choose the opposite door of whichever one they say.
Turns out, productivity soars when you have a well rested, well compensated, well treated, healthy, and housed people who don't have constant stessors of literally every aspect of their lives nearly crumbling beneath them...