Consider an LP with constraints Am 3 b, x 2 D. where A is an m x n matrix (with full row rank). Running the two-phase simplex method on such an LP...

Can you help me with two questions?

Q1: , prove that if the optimal value of (Q) is negative, then every certificate

of optimality y for (Q) is a certificate of infeasibility for the system Ax = b, x >= 0 (zero vector)

Q2: ) Suppose that when Phase 1 of the two-phase simplex method terminates, we determine

that the optimal value of (Q) is 0, and obtain an optimal solution (x1, ... , xn, 0,...,0(m zeros in total) )T,

prove that x : = (x1,..., xn)T is a basic solution to the system Ax = b, x >= 0 (zero vector)