Juliana is playing "Fifteen" by Taylor Swift. The length of the song is seconds. Juliana offers you the following bet: You may guess a value . Juliana will then stop the song at a uniformly random point along its duration. If the point at which she stops the song is at most seconds into the song, you must pay Juliana monetary units. Otherwise, she pays you monetary units. Find the value of that maximizes your expected profit.