What Is The Maximum?

Algebra Level 5

If x,y,zx, y, z are real numbers such that x+y+z=3 x + y + z = 3 , what is the maximum value of

2x+13+3y+53+8z+124? \sqrt{ 2x+13} + \sqrt[3]{3y+5} + \sqrt[4]{8z+12}?


This question was posed in SMO 2012. I came across it and it was interesting.
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