a$)$ Warm$-$Up

In 'Network City', the fire station is located at node s$.$ The city consists of nodes, where node $\backslash ($ s $\backslash )$ represents the fire station, and the remaining nodes represent houses in the city. Each house is connected by a road and the fire station has a map of the city that outlines the connections. When there is a fire in one of the houses, the fire station dispatches a firetruck to reach the house as quickly as possible.

Write the MCFNP model to find the minimum distance from $\backslash ($ s $\backslash )$ to $6$ and path corresponding to that distance. And by that we mean only indicate $\backslash ($ b $\backslash )$ and $\backslash ($ u $\backslash )$ values on the graph $(\backslash ($ c $\backslash )$ is already there$).$

b$)$ Two Stations

Following complaints that a fire station is insufficient, the city has opened a second fire station at node s$2$ and constructed new roads to improve accessibility. Now, fires have broken out simultaneously at houses $4$ and $7.$ You need to send a fire truck to both of the locations. Moreover, there is one fire truck available on $\backslash ($ s $1\backslash )$ and one more on s$2,$ so you have to send one fire truck from each of the locations. Model this problem as an MCNFP problem so that the total distance covered is minimized by both of the trucks. Most of the c values are already there, but you need to define additional nodes and c values for them. Moreover, indicate $\backslash ($ u $\backslash )$ and $\backslash ($ b $\backslash )$ values for rest of the graph as well.

c$)$ Network Simplex

For Part b$,$ first find a non$-$optimal basic feasible solution, and then apply one iteration of network simplex. You do not need to achieve the optimal solution.