This question is asking for the minimum amount of cable needed to connect the nine locations based on the graph provided. This is a classic Minimum Spanning Tree (MST) problem, which can be solved using algorithms such as Kruskal's or Prim's algorithm. The goal is to connect all the nodes (locations) with the minimum total cable length, which corresponds to minimizing the sum of edge weights.

I'll now calculate the minimum spanning tree of the graph provided in the image to determine the minimum total cable length needed.

Steps to solve:

1. List all the edges and their corresponding weights.
2. Use Kruskal’s algorithm:
   • Sort the edges by weight (in ascending order).
   • Add the smallest edge that doesn’t form a cycle to the MST.
   • Repeat until all locations are connected (number of edges = number of nodes - 1, i.e., 8 edges here).

I will now calculate the MST.