my problem is related to linear programming or operations research

all are very short please do all

2) We have a primal problem of the form max c7 x subject to Axsb and its associated dual problem. Assuming that the primal problem admits an optimal solution, show that at least one of the two domains (dual or primal) is unbounded. 3) Show that if a problem is unbounded, infeasibility is generated in the dual problem. Determine a certificate of such infeasibility based on conditions of no primal bounding. 4) Let P) be a linear optimization problem whose relaxed domain is equal to its convex envelope. If the linear relaxation of P) has multiple optimal solutions, then P) has at least two optimal solutions. True or False? Justify