Consider a generic LP in standard form: minimize cu subject to Ax = 6 (LP) > 0, where c, IER, A Rmx, and be RM. In addition, A is assumed to have full row rank. As an alternative to the two-phase approach, consider using the big-M method to solve (LP): m minimize +2+Mu subject to Ac +r" = b (bigM) #,">0, where x = (11,....) is a vector of artificial variables, and M is a large constant. If (bigM) is solved by the simplex method, prove the following: (4.a) If an optimal solution is found with r" = 0 (a zero vector), then the corresponding x is an optimal basic feasible solution to the original problem. (5 pt) (4.b) If for every M > 0, the problem (bigM) is unbounded, then the original problem is either unbounded or infeasible. (7 pt) (4.c) Let U* denote the optimal objective function value of (LP), and V"(M) be the optimal objective function value of (bigM), with a given M > 0. Show that V*(M) 0. (8 pt) Consider a generic LP in standard form: minimize cu subject to Ax = 6 (LP) > 0, where c, IER, A Rmx, and be RM. In addition, A is assumed to have full row rank. As an alternative to the two-phase approach, consider using the big-M method to solve (LP): m minimize +2+Mu subject to Ac +r" = b (bigM) #,">0, where x = (11,....) is a vector of artificial variables, and M is a large constant. If (bigM) is solved by the simplex method, prove the following: (4.a) If an optimal solution is found with r" = 0 (a zero vector), then the corresponding x is an optimal basic feasible solution to the original problem. (5 pt) (4.b) If for every M > 0, the problem (bigM) is unbounded, then the original problem is either unbounded or infeasible. (7 pt) (4.c) Let U* denote the optimal objective function value of (LP), and V"(M) be the optimal objective function value of (bigM), with a given M > 0. Show that V*(M) 0. (8 pt)