Peter is risk-neutral.

He can invest an amount of $x into a project.

The project is successful with probability \sqrt{x/1600}, where x is the number of dollars Peter has invested.

If successful, the project pays Peter $3200, otherwise nothing.

The project takes place in a country on the verge of civil war. Peter thinks there is a 10% chance that a civil war will break out so that Peter will be unable to claim any payments of a successful project, leaving Peter with nothing.

What is the optimal investment into the project if Peter is maximizing expected payoff?

Possible answers: (0, 36, 49, 81, 108, 252, 288, 324, 432, 594, 729, 810, 1296, 1336, 1801, 2025, 2525, 2732, 2916, 3281, 4900, 5625, 8100, 9000)