3. Lucy is addicted to nicotine. Her utility from smoking c cigarettes (net of their cost) is given by 1 Urm) ZZV'Eir: Her sister Tammy prefers a healthy lifestyle, her favorite commodity is kalejuice, j. The two sisters live together and Tammy is exposed to second-hand smoke, so her utility is adversely affected by Lucy's consumption of cigarettes. In particular, her utility function (net of cost of kale juice) is given by 1 UT . = 3 ._ __. (1.0) 1!} c 2} (a) Find the consumption of cigarettes that maximizes the Lucy's utility. Find the consumption of kalejuice that maximizes Tammy's utility. (Note: since these are net of cost, you simply need to solve unconstrained maximization problems. In other words, find the marginal utilities, set equal to zero, and solve). {b} Find the Pareto efcient level of cigarettes (c) and kale juice (j). HOW does the value of c differ from your answer in (a)? Why