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In numbers what is the maximum possible utility person 1

Suppose there are two persons, 1 and 2, who consume one good in the quantities x1 and x2, respectively, whereby x₁+ x2 = X = 10. The utility functions of 1 and 2 are respectively:

u₁= 4x₁

u₂= 4 (lnx₂)

In numbers, what is the maximum possible utility person 1 could achieve ie., if 1 gets all X?
If x₁= 10 - e², what is the maximum value of person 2's utility?
Find the equation of the UPF. Express this equation with u2 on the left and everything else including u₁ on the right (this expression will contain ln).
Write the equation of the utilitarian social welfare function, W, in terms of x₂
According to utilitarianism, what is the social welfare maximizing allocation to person 2, x₂*?
According to utilitarianism, what is the social welfare maximizing allocation to person 1, x₁*?
What is the maximum numerical value of social welfare, W*?

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