Problem
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 carbon emission and global warming at most k servers can stay functional at a time. Our objective is to find the optimal set of k servers so that each client can be served while minimizing the total service cost. Let OPT be the sum of the service costs over all clients for the optimal solution.
a) Design an LP representing the problem. [Clearly describe in language the variables, describe the constraints and objective function]
b) Write the dual LP.