Consider the following LP model: Max z= 5x1 + 4x2 + x3 s.t. x1 + x2 + x3 50 2x1 - x2 + x3 15 x1 + x2 = 10 x1 0, x2 urs, x3 0 a) (6 points) Write the dual problem. b) (3 points) If the primal problem is infeasible (has no solution), what would you conclude about the dual problem? c) (6 points) If the optimal Primal solution is x*=(A, B, C) and optimal Dual solution is y*=(1,D,E), find the values of A, B, C, D and E using the Complementary Slackness conditions without using the Simplex Algorithm. Show that strong duality property holds