A city is facing a fire station problem. Specifically, you are asked to help figure out where to locate fire stations in this city. The city consists of 5 different districts. A fire station can be placed in any district and is able to handle emergent fires for both its district and any adjacent district (i.e., any district with a non-zero border with its home district). The city has to find the minimum number of fire stations needed to cover all districts (i.e., each district is covered by at least one fire station). (a) Formulate algebraically this BIP problem. Define the decision variables, objective function, and constraints. DO NOT SOLVE. (10 points) (b) Suppose an additional requirement is imposed: If a fire station is placed in district 5, then there must also be a fire station placed in district 1 and 4 . Write down the constraint algebraically. ( 2 points) (c) Suppose an additional requirement is imposed: If a fire station is placed in district 2, then there must also be a fire station placed in district 4 and no fire station can be placed in district 3 . Write down the constraint algebraically. ( 2 points)