2. (15 points) Consider the following linear program: max 35 x1 + 45 x2 s. t. 3 x1 + 7 x2 >= 21 3 x1 >= 15 -10 x1 -

18 x2 >= -144 —Зх1 — 2х2 >= -36 x1 + x2 < =14 x1 >= 0, x2 >= 0 a) Graph the feasible region of the LP. Is the feasible region unbounded? b) Are any of the above constraints redundant? If so, indicate which one(s). Why would you want to eliminate redundant constraints? c) Solve the problems using the graphical method. Explain your approach and solution. d) Suppose we add the constraint 3 x1 + 2 x2 > a to LP. For which values of a: Is the constraint redundant? The problem becomes infeasible? The optimal solution found above is no longer optimal? e) Using the original problem, replace the objective function with the objective function 35 x1 + ß x2, and find the values of ß for which your previous optimal solution is no longer optimal.