Question: Consider the following linear program: max x1 +2x2 s.t. x1 x2 2 x1 + x2 4 x1 2.5 x2 3 x1, x2 0 (a) Graph

Consider the following linear program: max x1 +2x2 s.t. x1 x2 2 x1 + x2 4 x1 2.5 x2 3 x1, 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). (c) Solve the LP using the graphical method. Explain your approach. (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 2x1 + x2 to (LP). For which values of : is the constraint redundant? the optimal solution found above is no longer optimal? the problem becomes infeasible? Use the graph of the feasible region drawn in Part (a) to answer these questions.

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