Consider the following problem.

Maximize Z  3x1  2x2, subject to 3x1  x2 12 x1  x2 6 5x1  3x2 27 and x1 0, x2 0.

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(a) Solve by the original simplex method (in tabular form). Identify the complementary basic solution for the dual problem obtained at each iteration.

(b) Solve the dual of this problem manually by the dual simplex method. Compare the resulting sequence of basic solutions with the complementary basic solutions obtained in part (a).