Question 3: Consider the integer programming problem min (0,33) at Am 2 b, (l) a: 2 0, :2: integer, in which the matrix A has integer entries. Prove that its optimal value is not smaller than the optimal value of the linear programming problem max ([6], A) s.t. ATA S c, A 2 0. The symbol [1)] denotes the roundup of the vector b: the smallest integer vector greater than or equal to b