Consider the following linear program: 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). (For large linear problems, eliminating redundant constraints can speed up the solution of the linear program.) c) Solve the problems using the graphical method. Explain your approach and solution. d) Is there more than one optimal solution? If so give two different solutions. If not, explain using the graphical method why not. e) Suppose we add the constraint 2x_1 + x_2 gaterthanorequalto alpha to LP. For which values of alpha: Is the constraint redundant? The optimal solution found above is no longer optimal? The problem becomes infeasible? To answer these questions use the graph of the feasible region drawn in Part a) f) Replace the objective function x_1 + 2x_2 with the objective function x_1 + beta x_2, and compute the values of beta for which the point (2.5,1.5) is optimal