Formulate the shortest path problem as a linear programming model. Clearly define all sets, parameters, decision variables, the objective function, and constraints. $(10$ points$)$

$(40$ points$)$ Use the $n_{{?}^{?}}(th)-$nearest algorithm discussed in the lecture for undirected graphs to find the shortest path between the $0-$T nodes through each of the following networks. The numbers represent actual distances between the corresponding nodes.

$($b$)$