Subject / Operation Research

You need to visit a city you have never been to before and you want to reach that city by the shortest route. That's why you work on the map to determine the shortest path. Depending on the route you choose, you have to pass through different cities (cities that can be passed: A, B, C, D, E). Table 3 shows the distance (kilometers) between adjacent cities. Answer the following questions regarding this shortest path problem.

a)Create the network representation

b) Write the mathematical model.

c) Solve with Dijkstra's algorithm.

\begin{tabular}{|c|c|r|r|c|c|c|} \hline \multirow{2}{*}{ Cities } & \multicolumn{6}{|c|}{ Distance Between Adjacent Cities } \\ \cline { 2 - 7 } & A & B & C & D & to & Arrival \\ \hline Beginning & 40 & 60 & 50 & - & - & - \\ \hline A & & 10 & - & 70 & - & - \\ \hline B & & & 20 & 55 & 40 & - \\ \hline C & & & & - & 50 & - \\ \hline D & & & & & 10 & 60 \\ \hline TD & & & & & & 80 \\ \hline \end{tabular}