2. (33 pt) Consider the following linear programming problem minimize -2.11 - 3.02 + 4.83 subject to 11 + 2.12 0. (2a) Write out the dual problem of the above LP problem. (4 pt) (2b) Use the duality theories (weak duality, strong duality and complementarity slackness) to find the optimal primal and dual solutions, respectively. (Note that you can use the graphical approach to find an optimal solution of one problem and use duality theories to find an optimal solution of the other.) (9 pt) (2c) Based on the optimal primal solution you identified in (2b), write out the optimal tableau of the primal problem. (Please explain how you obtain the values of the entries in the optimal tableau. Note that solving the problem from scratch using the simplex method to obtain the optimal tableau will not earn you any credits.) (8 pt) (20) Let b and b2 denote the right-hand side of the first two constraints in the above LP; that is, b1 = 12 and b2 = 8. Within what range of b such that the primal optimal solution will remain optimal? (4 pt) (2e) Now suppose that b2 is changed from 8 to 16. Re-solve the problem using the dual simplex method. (Note that you must use the dual simplex method.) (8 pt)