5. [25 POINTS] Suppose Mary's preferences over 3:1 and :32 are summarized by the utility function u (:1, $2) = $9.5 + 223-5 As usual, She has a total income of $m available to spend on :31 and 3:2 at prices p1 and pg per unit, respectively. (a) [5 POINTS] Find her marginal rate of substitution (M R83, '12). [b] [10 POINTS] Derive her demand functions 3:; (131,132,171) and at; (p1,p2,m) by using the method of Lagrange. [c] [10 POINTS] Now assume her income is m = $2880 and the price of good 2 is p2 = $1 per unit. Find the quantities of :31 and 3:2 that Mary will choose to buy if p1 = $9 and if p1 = $4