1. Consider a decision maker who is choosing how many apples to buy. His choice set is {0, 1, 2, 3, 4, 5, 6} (the store has only 5 apples). (a) Suppose the decision maker always wants as many apples as possible. Find a utility function that represents this preference. (b) Suppose the decision maker always wants as few apples as possible. Find a utility function that represents this preference. (c) (A bit trickier) suppose the decision maker’s ideal number of applies is 3, and he is indifferent between m < 3 apples and 6 − m. Find a utility function that represents this preferences.