3. (15 points) Consider the following linear program: f) Graph the feasible region of the LP. Is the feasible region unbounded? g) 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.) h) Solve the problems using the graphical method. Explain your approach and solution. i) Suppose we add the constraint x, + 2x2 > 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? j) Using the original problem, replace the objective function with the objective function 15 x1 + ß x2, and find the values of ß for which the point (1, 2.5) is the optimal solution.

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7

Fig: 8

Fig: 9

Fig: 10