$9\mathrm{.}2-12.$ 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. Bagin with why this occurs when the north$-$

west corner rule is used. $($Similarly$,$ the general initialization proce$-$

dure presented in Supplement $2$ to this chapter can only construct

any integer BF solution to be the initial BF solution.$)$ 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 these observations for the transportation simplex

method imply that the integer solutions property presented in

Sec. $9\mathrm{.}1$ must hold.