$($Ambulance Siting Problem$)$ The nine communities on the road network shown below are all part of the same

rural county. Travel times between pairs of communities are shown on the arcs of the network $($in minutes$).$

They have banded together to form a single ambulance service to serve all nine towns with the eligible sites for

ambulances restricted to any of the nine communities. The county council desires to site the least number of

ambulances such that all of the towns can be reached within $15$ minutes.

a$.$ Set up and report the integer programming model to achieve the county$$s objective.

b$.$ Solve the LP relaxation using Pyomo. Solve the IP using Pyomo. Are the results different?

c$.$ Add a constraint that says at most $1$ ambulance can be placed in locations $3$ and $8$ combined. Re$-$solve the

LP relaxation and the IP$.$ What happen with the results now?

d$.$ Attempt to round the solution obtained from the LP from part c and compare your results with the IP

solution from part c$?$