Consider the following linear programming model:

Maximize X +2Y

Subject to

(1) 2X - 2Y 4

(2) X + Y 4

(3) 2X 5

(4) Y 4

X, Y 0

1. Graph the constraint lines and mark them clearly with the numbers (1), (2), (3) and (4) to indicate which line corresponds to which constraint. Darken the feasible region. Is the feasible region unbounded? .

1. Is there any redundant constraint? If so, indicate which one(s).
2. Determine the optimal solution(s) and the Maximum value of the objective function using the objective function line method (Show your calculation).

1. What other method can you choose to find the optimal solution without drawing the objective function? Considering the structure of the feasible region, which method is better? Justify your answer.

1. Is there more than one optimal solution? If so, give the two alternate solutions. If not, explain using the graphical method why not?

1. Use the graph of the feasible region drawn in Part (a) to answer the questions below:

Suppose we add the constraint 2X + Y to the linear programming model.

For what values of :

1. the optimal solution found above (in part (c)) is no longer optimal but remains feasible? Show your work.
2. the linear programming model becomes infeasible? Show your work.