Consider a scenario where C is the set of clients and S is the set of servers. Each client i in set C can be served by server j in set S with a service cost ci j . Because of the emerging issue of...

· responsible for serving a given client. This can be modeled using the constraint "sum j in S x i,j = 1, forall I in C." This can be used to illustrate the concept.
· The second limitation is that there can only be a maximum of k servers in use, and this limitation can be represented by the following constraint: "sum i in C x i,j leq k, forall j in S." Last but not least, we need to make sure that none of the variables have a negative value. This need can be expressed as the constraint x i,j geq 0, forall I in C, j in S. This will ensure that all of the variables have a positive value.
· The final stage is to define...