Solve the following problems by the fractional cut, and compare the true optimum integer solution with the solution obtained by rounding the continuous optimum.
*(a) Maximize z = 4x1 + 6x2 + 2x3
subject to
4x1 - 4x2 ≤ 5
- x1 + 6x2 ≤ 5
x1, x2, x3 ≥ 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 ≥ 0 and integer