Paul likes two scoops of vanilla ice cream for every chocolate scoop. He gets no extra utility for an additional chocolate scoop if he doesn't have two additional vanilla scoops and no extra utility for extra vanilla scoops without the appropriate amount of chocolate. His utility function can be represented by:

1. (,) = + 2
2. (,) = min{2,}
3. (,) = min{, 2}
4. (,) = 2 +
5. None of the above

Which of the following utility functions does not represent the same preference?

a. u = xy

b. u = (xy)^1/2

c. u = (xy)^-1

d. u = 2(xy) + 10

e. None of the above.

3. If an individual's utility function is given by and M = 100, px = 1, py = 4, his or her preferred consumption bundle will be:

a. (20, 20).

b. (50, 12.5).

c. (40, 15)