Meeting rooms on university campuses may or may not contain coff ee machines. We wouldlike to ensure that every meeting room either has a coff ee machine or is close enough to ameeting room that does have a co ffee 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 coff ee machines so that weuse as few co ffee machines as possible. Specify this problem as an optimization problem on agraph. Formulate the corresponding Coff ee-machine Decision Problem (abbreviated Coff ee).Prove that the Coff ee Machine Decision Problem is NP-complete.
Hint: You could use Vertex Cover. For every edge, add two more edges and one more vertex.
