Consider a linear programming formulation in standard form: mins.t.cxAx=b,x0. where cn,Anm, and bm. 1 - Question for student 1: Given any basis matrix B of matrix A. Prove that the above linear programming problem can be reduced to a linear programming problem with only nonnegativity constraints. Further show that a constraint qualification holds for all the KKT solutions to this new linear programming formulation. - Question for student 2: For a basic feasible solution, prove that having non-negative reduced costs implies the satisfaction of the KKT conditions. Consider a linear programming formulation in standard form: mins.t.cxAx=b,x0. where cn,Anm, and bm. 1 - Question for student 1: Given any basis matrix B of matrix A. Prove that the above linear programming problem can be reduced to a linear programming problem with only nonnegativity constraints. Further show that a constraint qualification holds for all the KKT solutions to this new linear programming formulation. - Question for student 2: For a basic feasible solution, prove that having non-negative reduced costs implies the satisfaction of the KKT conditions