Bob goes to a grocery store that only sells water, juice, and soda. Bob likes having more water than having less water, having more juice than having less juice, and having more soda than having less soda. Ignoring his budget constraint, assume that Bob is always able to choose the single most preferred bundle out of a given menu.

1. (a)Suppose Bob's choice patterns are as follows:
2. ?If offered{10 oz of water, 10 oz of juice}Bob chooses 10 oz of water.?If offered{10 oz of juice, 10 oz of soda}Bob chooses 10 oz of juice.
3. ?If offered{10 oz of water, 10 oz of soda}Bob chooses 10 oz of soda.
4. Do Bob's preferences violate any of the axioms of rational choice? If so, what should change to fix the violation?
5. (b)Bob's friend Laura goes to the same store. Assume that Laura is always able to choose the single most preferred bundle out of a given menu.
6. ?If offered{10 oz of water, 10 oz of juice}Laura chooses 10 oz of water.?If offered{10 oz of soda, 10 oz of juice}Laura chooses 10 oz of soda.?If offered{10 oz of soda, 10 oz of water}Laura chooses 10 oz of soda.
7. Do Laura's preferences violate any of the axioms of rational choice? If so, what should change to fix the violation?
8. (c)Suppose Bob's friend Alex, who goes to the same store, choice patterns are as fol- lows:

• ?Alex is offered the bundles
• {(10 oz of water+10 oz of soda), (10 oz of juice + 10 oz of soda)}and chooses (10 oz of water+10 oz of soda).
• ?Alex is offered the bundles
• {(9.9999 oz of water+10 oz of soda), (10 oz of juice + 10 oz of soda)}and chooses (10 oz of juice + 10 oz of soda).
• Given the fact that Alex always chooses the more preferred bundle, which axiom is evidently violated? Explain.