Mike finds a Coke machine in an abandoned part of town and is extremely thirsty. The Coke machine requires exact change -two quarters and a dime. No other combination of coins will make anything come out of the machine. No stores are open where he can make change. Mike will buy as many soft drinks as he can with whatever change he has; the more soda he can buy, the better. Consider Mike's preferences for quarters and dimes.

a. Draw a graph that illustrates all the combinations of quarters and dimes the Mike will treat as indifferent to having 2 quarters and 1 dime. Then draw another graph illustrating all the combinations of bundles and dimes that mike treats as indifferent to having 4 quarters and 2 dimes.

b. Does Mike have convex preferences for quarters and dimes?

c. Does Mike always prefer more of both kinds of money to less?

d. If Mike where holding 7 quarters and 2 dimes how many dimes would you have to give him to give up one quarter? Explain your reasoning.

e. If Mike where holding 2 quarters and 2 dimes how many dimes would you have to give him to give up one quarter? Explain your reasoning.