l. [10] Meursault purchases a dozen eggs and must take them home. Although making trips home is costiess, there is a 50 percent chance that all of the eggs carried on any one trip will be broken during the trip. The individual considers three strategies: strategy 1: take all 12 eggs in one trip strategy 2: take two trips with six eggs each strategy 3: take four trips with three eggs each a} List the possible outcomes of each strategy and die probabilities of these outcomes. Show that on the average, six eggs will remain unbroken after the trip home under each strategy. 3 points. b) List the lotteries that each strategy generates and the expected utility of each strategyflottery for Meursault's utility Lite}. 3 points. Suppose that a trip now costs T, and let utility be given by at?) = e\" - .f r where .f is the number of trips. I: the number of eggs he successfully brings home, and o e 1 is a constant. c) Which strategy yields the highest expected utility. as a function of 1- and a? What happens as r rises? as (1' declines? 4 points