Define decisin variable, objective function and constraints

problem 2. A certain state allows a restricted form of branch banking. Specifically, a bank can do business in county i if the bank has a PPB (principal place of business) in county i or in a county sharing a nonzero-length border with county i. The following Figure is a map of the state in question. For example, if the bank has a PPB in county A, then it can operate in counties A, B, and D. As another example, if the bank has a PPB in county E, it can operate in counties B, C, E, F, G, J, and H. Formulate the problem of locating a minimum number of PPBs (principal places of business) in the state, so a bank can do business in every county in the state. K A C F B E G D H J