Explain what is meant by a transportation problem where the total demand equals the total supply. Write the Lagrangian and describe an algorithm for solving such a problem. Starting from the north-west initial assignment, solve the problem with three sources and three destinations described by the table

\begin{tabular}{|rrr|r|} \hline 5 & 9 & 1 & 36 \ 3 & 10 & 6 & 84 \ 7 & 2 & 5 & 40 \ \hline 14 & 68 & 78 & \ \hline \end{tabular}

where the figures in the $3 \times 3$ box denote the transportation costs (per unit), the right-hand column denotes supplies, and the bottom row demands.