5. [25 POINTS] Suppose Mary's preferences over 3:1 and 1122 are summarized by the utility function \"(11'3\" = T As usual, she has a total of $171 available to spend on 2:1 and $2 at prices p1 and pg per unit, respectively. (a) [5 POINTS] Find her marginal rate of substitution (M RS,y). (b) [10 POINTS] Derive her demand functions1 If (p1, pg, 171) and :3; (pl, 192, m} by using Lagrangian mul- tiplier. (e) [10 POINTS] Now assume her inmme is m = $288 and the price of good 2 is p2 = $1 per unit. Find the quantity of $1 and I2 that Mary will choose to buy if p1 = $9 and if 391 = $4