(Solution) - Investigate the optimality of the TOYCO solution for each of -(2025 Original AI-Free Solution)

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Investigate the optimality of the TOYCO solution for each of the following objective functions. If the solution changes, use post-optimal analysis to determine the new optimum.
(The optimum tableau of TOYCO is given at the start of Section 4.5.)
(a) Z = 2x1 + x2 + 4x3
(b) Z = 3x1 + 6x2 + x3
(c) Z = 8x1 + 3x2 + 9x3