In the realm of renewable energy, a challenge has arisen in optimizing the transmission of electricity from various solar and wind farms to major power distribution centers across the United States. A network of existing transmission lines and the locations of key distribution centers are laid out in the attached Figure $($ see the attachment below $).$ ?The primary goal is to identify and revitalize specific transmission lines to efficiently connect the solar and wind farms with the distribution centers. In particular, the high $-$ capacity distribution center in Los Angeles $($ LA $)$ ?must be linked directly to the distribution center in Chicago $($ CH $)$ ?to handle the anticipated increase in renewable energy production. Other than that, all the remaining centers can be linked, directly or indirectly, such that the total length $($ in miles $)$ ?of the selected transmission lines is minimized. Determine the segments of the transmission lines that must undergo revitalization to ensure a streamlined and eco $-$ friendly energy distribution network.