Hello, I need help with problems 8-11. 1-7 I have done, they are just there for reference. thank you

Suppose there are two persons. I and 2, who consume one good in the quantities x, and Jr2 , respectively, whereby x, + II = X = 10. The utility functions of l and 2 are, TCFPCL'Ii'I cig: at, = 4x] a, = 4 - In x, 1. In numbers, what is the maximum possible ntilit}.r person l could achieve, i.e.. if 1 gets 3111'? 2. if 1, =19 e2 , what is the maximum 1ralue ofperson 2's utility? 3. Find the equation of the Utility Possibilities Frontier. Express this equation with a, on the left and everything else including a, on the right (do not simplify this expression will contain In). 4. Write the equation of the utilitarian social welfare function, W, in terms of x1 (this expression will contain in). 5. According to utilitarianism, what is the social welfare maximizing allocation to person 2, x; ? 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\"? For the following problems, consider the set up above with one single change, via, there is an added term in person 2's utility function reecting 2's warm glow altruism toward 1: at2 =4tlnx2 +Jrl Simplify any numerical solutions, but do not round. Note that certain solutions indicated below will be expressed in terms containing 1n. 8. Find the equation of the Utility Possibilities Frontier with a, on the left and everything else including it, on the right. 9. Write the equation of the utilitarian social welfare function, W, in terms of 1:1. Simplify but keep In in the expression. 10. What is the social welfare maximizing allocation to 2, x; , according to utilitarianism? 11. What is the social welfare maximizing allocation to l, x: , according to utilitarianism