Solve the following LPs by the revised simplex method:

(a) Maximize z = 6x1 - 2x2 + 3x3 subject to 2x1 - x2 + 2x3 … 2 x1 + 4x3 … 4 x1, x2, x3 Ú 0

(b) Maximize z = 2x1 + x2 + 2x3 subject to 4x1 + 3x2 + 8x3 … 12 4x1 + x2 + 12x3 … 8 4x1 - x2 + 3x3 … 8 x1, x2, x3 Ú 0

(c) Minimize z = 2x1 + x2 subject to 3x1 + x2 = 3 4x1 + 3x2 Ú 6 x1 + 2x2 … 3 x1, x2 Ú 0

(d) Minimize z = 5x1 - 4x2 + 6x3 + 8x4 subject to x1 + 7x2 + 3x3 + 7x4 … 46 3x1 - x2 + x3 + 2x4 … 20 2x1 + 3x2 - x3 + x4 Ú 18 x1, x2, x3, x4 Ú 0