There are two (equally prevalent) types of workers, creative and obedient. After finishing college each worker chooses how many months x [0,12] to travel the world before applying for a corporate job. The utility a creative type gets from travel is 2x. The utility an obedient type gets from travel is x. After they are done with the travels, they apply for a job. The rm is only willing to hire a worker if it thinks he is certainly obedient. The payoff to any worker from being hired is 20. The payoff from not being hired is 0. To these payoffs we add the utility from travel to get the worker's overall payoff.

What is the highest payoff that an obedient type can get in any Perfect Bayesian Equilibrium?

What are the equilibrium strategies that yield that payoff?