When you deal with a transportation problem where the supply and demand quantities have integer values, explain why the steps of the transportation simplex method guarantee that all the basic variables (allocations) in the BF solutions obtained must have integer values. Begin with why this occurs with the initialization step when the general procedure for constructing an initial BF solution is used (regardless of the criterion for selecting the next basic variable). Then given a current BF solution that is integer, next explain why Step 3 of an iteration must obtain a new BF solution that also is integer. Finally, explain how the initialization step can be used to construct any initial BF solution, so the transportation simplex method actually gives a proof of the integer solutions property presented in Sec. 9.1.
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