Consider a minimum cost network flow problem instance with five nodes. Suppose node 1 has a supply of 32 units, node 4 has a demand of 22 units and node 5 has a demand of 10 units. The remaining nodes (nodes 2 and 3) are transshipment nodes. The arcs of the network with their capacities and unit cost values are provided in the table. a-Formulate the problem as a linear program.

\begin{tabular}{c|c|c} \hline arc & capacity & cost (\$ per unit flow) \\ \hline(1,2) & 25 & 15 \\ (1,3) & 12 & 11 \\ (2,3) & & 5 \\ (2,5) & 20 & 10 \\ (2,4) & 30 & 5 \\ (3,4) & 12 & 4 \\ (3,5) & & 5 \\ (5,4) & & 14 \\ \hline \end{tabular}