Solve the following problems by the fractional cut, and compare the true optimum integer solution with the solution obtained by rounding the continuous optimum.

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(a) Maximize z = 4x1 + 6x2 + 2x3 subject to 4x1 - 4x2 … 5 -x1 + 6x2 … 5 -x1 + x2 + x3 … 5 x1, x2, x3 Ú 0 and integer

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