Exercise: Let us consider the set bipartitioning problem. Given a set X of n positive integers e1, e2, . .., e_n where n is an even value. The problem consists in partitioning the set X into two subsets Y and Z of equal size. Q1. How many possible partitions of the set X exist? An optimization problem may be defined as follows: Minimum set bipartitioning that consists in minimizing the difference between the sums of the two subsets Y and Z. Q2. Provide a mathematical formulation of this optimization problem. Q3. Given an instance of this problem of size 6, with the following integers X= {1,2,5,6,7,9). (a) enumerate all feasible solutions, and give the objective value for each one. (b) give an example of an infeasible solution. (c) what is the global optimal solution