Demonstrate graphically that this problem has no feasible solutions.

1. For the Big M method, explain why the simplex methodnever would choose an artificial variable to be an entering basi variable once all the artificial variables are nonbasic
2. Consider the following problem Maximize Z _ 90×1 _ 70x subject to

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2×1 _ x2 _ 2
x1 _ x2 _ 2and
x1 _ 0, x2 _ 0.
(a) Demonstrate graphically that this problem has no feasible solutions.
(b) Use a computer package based on the simplex method to determine that the problem has no feasible solutions.
(c) Using the Big M method, work through the simplex method step by step to demonstrate that the problem has no feasible solutions.
(d) Repeat part (c) when using phase 1 of the two-phase method