Khadija is planning a party and figuring out how much to spend on food (F) and entertainment (E). The guests all have similar utility functions U (F, E) = F 1 4 E 3 4 . a Find her optimal bundle of food and entertainment at prices PF , PE and a budget B. You may use either Lagrange method or the tangency method for finding the optimal bundle. b Now, rewrite Khadija's optimal bundle of food and entertainment in terms of prices (PF , PE ) and budget B. With optimal quantity of food on the y-axis and party budget on the x-axis, graph her Engel curve (Hint: For Engel curve, treat prices as fixed constants and vary only the party budget)