NP Complete

Meeting rooms on university campuses may or may not contain coffee machines. We wouldlike to ensure that every meeting room either has a coffee machine or is close enough to ameeting room that does have a coffee machine. (For any two meeting rooms, the architecthas told us whether or not they are close enough.) Our problem is to determine among all themeeting rooms of any university campus, which ones should have coffee machines so that weuse as few coffee machines as possible. Specify this problem as an optimization problem on agraph. Formulate the corresponding Coffee-machine Decision Problem (abbreviated Coffee).Prove that the Coffee Machine Decision Problem is NP-complete.

Hint: You could use Vertex Cover. For every edge, add two more edges and one more vertex.