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$.$ Using the intuitive method, what the the total cost of the initial solution?

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c$.$ Based on the Stepping Stone Method $($solver$),$ what is the optimal solution? $

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d$.$ If $10$ units were required to be shipped from S$1$ to D$1,$ what would be the overall cost?