A student is maximizing his productivity given by the function P(x, y) = x2ey, where x and y are the number of hours of working on academics and hobbies, respectively. In 24 hours, how many number of hours must the student spend working on hobbies to maximize his productivity? (Use Lagrange multipliers)   note: x = number of hours working on academics y = number of hours working on hobbies

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