Please write out all the steps on a separate piece of paper cause when it is written on the laptop, it gets confusing to understand what is happening. Appreciate it! Thanks!

Problem 3 (a) Suppose that when Jane is presented with the following two menus, her choices from them are as below 2 0 When presented with the menu {6 units of apples, 5 units of bananas}, Iane chooses 6 units of apples. 0 When presented with the menu {7 units of oranges, 5 units of bananas}, Iane chooses 5 units of bananas. Suppose that Jane is then presented with the menu {7 units of oranges, 6 units of apples} What must Jane's choice be from this menu so that her behavior conforms to the axioms of rational choice? Explain. (b) Suppose that Frederick choices from the following menus are as follows O For anys > 0 3, out of the menu {(4 + E apples and 3 bananas), (5 oranges and 3 bananas)}, Frederick chooses (4 + s apples and 3 bananas). ' Out of the menu {(4 apples and 3 bananas), (5 oranges and 3 bananas)}, Fred- erick chooses (5 oranges and 3 bananas) What axiom of rational choice does Frederick's behavior evidently violate? Discuss. 2Jane can choose only from the menu presented. 35 can be made arbitrarily small but strictly positive