The U$.$S$.$ Air Force $($USAF$)$ has enlisted your assistance in locating a network of new strategic defense assets $($SDAs$)$ across the continental United States. USAF has determined that the assets will be located only in major cities, and has identified $29$ major cities as prospective locations. Each of the $29$ cities need not have an SDA in it$,$ but all of the $29$ major cities must be located within $1000$ miles of a city in with an SDA in order for the network to provide sufficient defense of the entire country.

Attached to this assignment is a spreadsheet containing the distance between each of the $29$ cities and all of the other cities for you to use in your work

a$.(50$ points$)$ Using linear, integer, or mixed integer programming, determine the minimum number of locations for the new SDAs and the cities in which the USAF should located the SDAs. In doing so$,$ assume that the costs to install the SDAs are the same regardless of the locations that are selected.

b$.(50$ points$)$ As is common when it comes to allocating national resources, politics has come into play. Because of the economic impact of having these new assets in a city, powerful and influential leaders in Congress would like to make sure that the SDAs are equally distributed across so$-$called $$red$$ states $($those that politically lean toward Republicans in statewide and national elections$)$ and so$-$called $$blue$$ states $($those politically lean toward Democrats in statewide and national elections$).$