American Parcel Service $($APS$)$ has determined that it needs to add several new package distribution hubs to

service cities east of the Mississippi River. The company wants to construct the minimum set of new hubs in the

following $12$ cities so that there is a hub within $300$ miles of each city $($i$.$e$.,$ every city is covered by a hub$)$:

Use linear programming model to determine the location of hubs.