answer with constraints, & objective function

Nortex, the natural gas processing company for whom you previously determined a transshipment plan, has decided to expand its operations into the northeastern corner of Texas, via its subsidiary company Nortex East. To accommodate this expansion, the company has decided to hire several regional managers. Each manager will be based in one of the 25 counties in which Nortex East will operate and will provide oversight for the operations in that county and all adjacent counties that are directly accessible via a major roadway. If two or more managers have jurisdiction over a county, they will share the responsibility. Nortex East would also like to minimize the total amount it spends on the monthly base salaries of its managers. Base salaries are dependent on the county in which the manager is based, and are roughly related to cost of living and the total geographic area over which a manager would have jurisdiction. (Relocation subsidies, bonuses, and other costs are not included in the base salary.) In the case of shared jurisdiction as mentioned above, the overlapping managers will still receive the full monthly salary indicated. A map of Nortex East's business region and a table of counties, which includes information on the adjacent counties and associated monthly salaries, are provided on the next page. (Note that some counties border each other but are not directly accessible via a major roadway. The table indicates counties as adjacent if and only if they are accesible as such.) Thanks to your excellent work on their previous case, Nortex has once again chosen to partner with you to conduct an analysis and to make a recommendation that will help it to allocate Nortex East's regional manager positions such that each county has at least one regional manager assigned to it, while keeping the total cost of salaries to a minimum. In summary, you must develop a binary programming model, perform an appropriate analysis using Excel, recommend the counties in which Nortex East should place its area managers, and present a formal business report discussing your findings and conclusions. \begin{tabular}{l|r|l|r} County & # & \multicolumn{1}{|c|}{ Adjacent } & Salary (8) \\ \hline Grayson & 1 & 2,6 & 5,777 \\ Fannin & 2 & 1,3,6,7,8 & 9,813 \\ Lamar & 3 & 2,4,8 & 4,728 \\ Red River & 4 & 3,5,10,11 & 5,489 \\ Bowie & 5 & 4,12,13 & 6,076 \\ Collin & 6 & 1,2,7,14,15 & 6,832 \\ Hunt & 7 & 2,6,8,9,15,16,21,22 & 11,968 \\ Delta & 8 & 2,3,7,9 & 5,072 \\ Hopkins & 9 & 7,8,10,16,17 & 5,566 \\ Franklin & 10 & 4,9,11,17,18 & 7,270 \\ Titus & 11 & 4,10,12,18 & 4,264 \\ Morris & 12 & 5,11,13,19,20 & 7,132 \\ Cass & 13 & 5,12,20 & 3,998 \\ Dallas & 14 & 6,15,21 & 6,513 \\ Rockwall & 15 & 6,7,14,21 & 6,006 \\ Rains & 16 & 7,9,17,22 & 8,926 \\ Wood & 17 & 9,10,16,18,19,22,23 & 5,250 \\ Camp & 18 & 10,11,17,19 & 3,022 \\ Upshur & 19 & 12,17,18,20,23,24,25 & 12,409 \\ Marion & 20 & 12,13,19,25 & 3,422 \\ Kaufman & 21 & 7,14,15,22 & 7,313 \\ Van Zandt & 22 & 7,16,17,21,23 & 6,682 \\ Smith & 23 & 17,19,22,24 & 4,003 \\ Gregg & 24 & 19,23,25 & 6,174 \\ Harrison & 25 & 19,20,24 & 4,953 \end{tabular}