Explain with examples related to Freight Traffic Assignment Problems and vehicle routing problems in the logistics activities of manufacturing and service companies!

Solve the following case example using the transportation method:

Suppose there is a manufacturing company that produces and distributes their products to various customer locations across the country. This company has three production factories (Factory A, Factory B, and Factory C) located in different locations, and there are also five distribution centers (DC 1, DC 2, DC 3, and DC 4) spread across various regions.

The company's goal is to determine the most efficient transportation route to deliver products from factories to distribution centers, taking into account transportation costs and available capacity.

NOTE: Explain in detail, along with the formula.

Thank you.

\begin{tabular}{|l|c|c|c|c|c|} \hline \multirow{2}{*}{ Source } & \multicolumn{4}{|c|}{ Distribution Center } & \\ \cline { 2 - 6 } & DC 1 & DC 2 & DC 3 & DC 4 & Capacity \\ \hline Factory A & $145 & $150 & $165 & $140 & 2000 \\ \hline Factory B & $175 & $135 & $120 & $165 & 1250 \\ \hline Factory C & $113 & $156 & $134 & $148 & 1250 \\ \hline Demand & 1000 & 1200 & 1400 & 900 & \\ \hline \end{tabular}