These questions are related to the Quantitative Methods in Engineering Management:

Problem $4.$ The city planner is looking to connect five different neighborhoods to the central water treatment facility. Normally, water pipes would be laid directly from each neighborhood to the facility. However, due to the challenging terrain, the pipes need to be installed in a specialized, reinforced tunnel that is expensive but can carry up to five pipelines. To minimize the cost, use the minimal$-$spanning tree method to find the shortest tunnel route between the neighborhoods indicated in the network below. $($Note that the location of the central facility does not impact the solution.$)$

Neighborhood Connection Network with Distances