What is the maximum numerical value of social welfare

Question

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)

1. In numbers, what is the maximum possible utility person 1 could achieve ie., if 1 gets all X?
2. If x₁= 10 - e², what is the maximum value of person 2's utility?
3. 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).
4. Write the equation of the utilitarian social welfare function, W, in terms of x₂
5. According to utilitarianism, what is the social welfare maximizing allocation to person 2, x₂*?
6. According to utilitarianism, what is the social welfare maximizing allocation to person 1, x₁*?
7. What is the maximum numerical value of social welfare, W*?