A consumer consumes pizza and soda always in the fixed proportion of 3 slices of pizza (x) with 2 cups of soda (y). Any pizza or soda not consumed together with the proportional amount of the other is useless to her.

(a) Write down a utility function u(x,y) that represents her preferences.

(b) If she has I = $60 budget and px = 4, py = 4, what is her optimal bundle?

(c) In (b), If the price of soda increases to $6, how much money should she be compensated so that she achieves the same level of utility before the price increase?

(d) Returning to (b), If the price of soda increases to $6, how much should the price of pizza be reduced so that she achieves the same level of utility before the price hike?

(e) In (a), what values of a and b she is indifferent between the bundle "30 slices of pizza and a cups of soda" and the bundle "b slices of pizza and 40 cups of soda". Find at least two (a,b) pairs to get full points.