Find the minimum cost solution for the transportation problem detailed in the table below.

Costs D $1$ D $2$ D $3$ Supply

S $13012520$

S $210141230$

S $320112575$

Demand $406055$

a$.$ Is the transportation problem balanced

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$,$ if not, where is the unbalance

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$.$

b$.$ What is the optimal solution? $

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