A Manufacturer Wants to Construct Warehouses in Six Different Locations

Essay

A manufacturer wants to construct warehouses in six different locations of the city to supply dry cells to his customers on time. The manufacturer wants to construct the minimum number of warehouses such that each warehouse is within 40 miles of at least one other warehouse. The following table provides the distance (in miles) between the locations. $$\begin{array} { l c c c c c c } &&& { \text { To } } \\\hline \text { From } & \text { Location A} & \text { Location B } & \text {Location C } & \text { Location D } & \text { Location } \mathrm { E } & \text { Location } \mathrm { F } \\\hline \text { Location A } & 0 & 35 & 40 & 45 & 60 & 70 \\\text { Location B } &&0&35&40&70&75\\\text { Location C } & & &0&45&50&50\\\text { Location D } & & && 0&40&50\\\text { Location E } & & &&& 0 & 30& \\\text { Location F } & & & &&& 0\end{array}$$ Formulate and solve an integer linear program that can be used to determine the minimum number of warehouses needed to be constructed. What are their locations?