In the following problems, some of the variables have positive lower bounds. Use the bounded algorithm to solve these problems.

(a) Maximize z = 3x1 + 2x2 - 2x3 subject to 2x1 + x2 + x3 … 8 x1 + 2x2 - x3 Ú 3 1 … x1 … 3, 0 … x2 … 3, 2 … x3

(b) Maximize z = x1 + 2x2 subject to

-x1 + 2x2 Ú 0 3x1 + 2x2 … 10

-x1 + x2 … 1 1 … x1 … 3, 0 … x2 … 1

(c) Maximize z = 4x1 + 2x2 + 6x3 subject to 4x1 - x2 … 9 -x1 + x2 + 2x3 … 8 -3x1 + x2 + 4x3 … 12 1 … x1 … 3, 0 … x2 … 5, 0 … x3 … 2