5. (15 points) Consider the cooperative game with the following coalitional function. v(1) = 4, v(2) = 6, v(3) = 13, v(1, 2) = 21, v(1, 3) = v(2, 3) = 14, v(1, 2, 3) = 30. (a) Find the core, the least core (which 0 corresponds to it?). Provide the graphical representation of all conditions.

(b) Find the Shapley value.

(c) Find the nucleolus.