Question 1: For the following LP problem: max z = -2x1 - x2 + x3 s.t. x1 + x2 + x3 = 3 x2 + x3 2 2 + x3 = 1 X1, X2, X3 20 a) Write down the dual problem. b) After adding the loose variable ssl and artificial variables aa2 and aa3 to the primal problem and subtracting the redundant variable e2, the optimal basis is found to be BBW= {xx2, xx3, ss1}. Find the optimal values of dual variables using the Duality Theorem. (You are not allowed to use the simplex method for the dual problem in this question.)