I need proper written solution to this. It should be correct PLEASE. If you are not sure pls dont attempt.

Problem 1: Consider the utility function 1 u(x1,x2) = x1 + 3x: a) Find the demand functions for goods land 2 as a function of prices and income. f2(l71;102:m) m 3\" hpnpz) Note these demands will look likex , .371): { 2&1 p2 32(p1,pz,m) m 5 MPLPQ for some fu nctions f2, g2, and h; yourjob is to find these functions. b] Explain whythese demand functions do not necessarily satisfy the typical \"MRS equals relative price" condition. Include a graph in your answer. c) \"Income expansion paths are curves in (151,262) space along which MRS is constant." Is this statement true for these preferences? If so, what does it imply about the shape of the income expansion paths for these preferences? Include a graph in your answer. d] Explain using a graph why the income effect is zero for one of these two goods. e) Explain using a graph why compensating and equivalent variation are equal (CV = EV) for any price change. f] Graph the Engel curves for goods 1 and 2 with quantity on the vertical axis and income on the horizontal. Indicate the slope and horizontal intercept of each