1. Answer the following based on a utility function U(x,y) = x5 +y , Pr = Zand I; = 9. a) If income = 90, find the optimal quantity of the two goods. Now change income to 48 and try to solve this problem using the general method. Explain why the solution you get cannot be correct. (1 point) b) Draw an diagram with an indifference curve and a budget constraint to explain what is going on and nd the actual solution to the problem. (1 point) c) Find the demand functions for x (pimpy, ) and y (pmpwl) assuming both x>0 and y>0. (2 points) d) Explain from these functions why it will always be that x>0, but y>0 only if a condition is met. Show that condition. Also show the demand functions for x and y if the condition is not met. Explain how this result is consistent with part a. (2 points) e) Find the indirect utility function forthe case where y>0 and for where y=0. (1 point) f) Find the minimum expenditure associated with px=2, py=9 and a utility of 13. Explain why this answer is consistent with earlier results. (1 point)