The distances $($in miles$)$ between the Indiana cities of Gary, Fort Wayne, Evansville, Terre Haute, and South Bend are shown in Table $1.$ It is necessary to build a state road system that connects all these cities. Assume that for political reasons no road can be built connecting Gray and Ford Wayne, and no road can be built connecting South Bend and Evansville. What is the minimum length of road required? $($pp$.459,$ Answers: This minimum spanning tree has a total length of $414$ miles.$)$