If you plan to fold AK to his 3b then you may want to reconsider 3bettin this hand. If I were in UTG's spot, I would be shoving a much wider range than you listed because of ICM. There three stacks around 35-40bb and a short stack with 20bb and the tournament only pays the top 3. This allows the last aggressor in a pot between two of the larger stacks to put a lot of pressure on the other because none of you want to bust before the short stack. If UTG showed you 22 in this spot, it would be correct to fold because ICM outweighs the +cEV of calling. 

With that said, 3betting AK here can be good or bad depending on the width of UTG's opening range and how he will respond to a 3b. The ideal is that UTG opens wide and will respond to a 3b by 4b folding often. Another favorable case case is that he opens wide and will respond passively to a 3b by either folding or calling OOP. The least favorable situation is that he opens a tight range and will respond to a 3b by 4b a majority of his opens. Another more extreme case is that UTG is very loose and will respond to a 3b by 4b shoving a range wide enough that is is +tEV to call 3b call with AK. Use your reads on how UTG will react to a 3b and judge whether or not 3betting AK here is the best play.