Using the artificial constraint procedure introduced in Problem 4-37, solve the following problems by the dual simplex method. In each case, indicate whether the resulting solution is feasible, infeasible, or unbounded.

(a) Maximize z = 2x3 subject to

-x1 + 2x2 - 2x3 Ú 4

-x1 + x2 + x3 … 2 2x1 - x2 + 4x3 … 5 x1, x2, x3 Ú 0

(b) Maximize z = x1 - 3x2 subject to x1 - x2 … 20 x1 + x2 Ú 40 2x1 - 2x2 Ú 30 x1, x2 Ú 0

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(c) Minimize z = -x1 + x2 subject to x1 - 4x2 Ú 5 x1 - 3x2 … 1 2x1 - 5x2 Ú 1 x1, x2 Ú 0

(d) Maximize z = 2x3 subject to -x1 + 3x2 - 7x3 Ú 50 -x1 + x2 - x3 … 10 3x1 + x2 - 10x3 … 80 x1, x2, x3 Ú 0