Can you please write out utility functionc and provide explanation

3. Consider two people, Ann and Bernice, each of whom consumes only scoops of ice cream (21) and cones (12). Goods 1 and 2 are perfect com- plements for both Ann and Bernice. Ann only likes combinations of 1 scoop and 1 cone, while Bernice only likes combinations of 2 scoops and 1 cone. (a) Write out utility functions, u (21, 12) and u (21, 12), that satisfy Ann and Bernice's preferences, respectively. Show, by comparing two bun- dles, that v is not a monotone transformation of u. (b) Now consider Clarissa, who has very strange preferences over scoops and cones. Her utility function is max {:1, 12}. Draw some indiffer- ence curves that represent these preferences. (c) Interpret Clarissa's preferences in words. (d) Consider any budget line Clarissa might face. What can you say about where her optimal bundle must lie? 4. Consider the following preferences. Any two bundles, (11, 12) and (31, 92), can be compared according to the following rule: If x1 > y1, then (21, 12) > (y1, y2). If x1 = y1 and 12 > y2, then (21, 12) > (91, 92). (a) Show that these preferences cannot be represented by indifference curves (i.e. show that it is impossible to find two distinct bundles such that the consumer is indifferent between them). (b) Consider an individual who chooses his most preferred bundle ac- cording to these preferences. He faces some income (m) and prices (P1, p2). What will happen to his optimal bundle if the price of good 2 doubles