1. In class we covered the capacitated fixed-charge facility location problem. Rewrite the model formulation to account for a fixed set of possible facility types (e.g., small, medium, large) that can be built at each site. Each type has a certain capacity and a location-dependent fixed cost. Define the parameters, decision variables clearly. a Discuss how you might use Lagrangian relaxation to solve the above problem (#1). There is no need to actually implement it, but simply describe how you will define the multipliers, and write down the relaxed problem and possible ways to decompose/solve it. 1. In class we covered the capacitated fixed-charge facility location problem. Rewrite the model formulation to account for a fixed set of possible facility types (e.g., small, medium, large) that can be built at each site. Each type has a certain capacity and a location-dependent fixed cost. Define the parameters, decision variables clearly. a Discuss how you might use Lagrangian relaxation to solve the above problem (#1). There is no need to actually implement it, but simply describe how you will define the multipliers, and write down the relaxed problem and possible ways to decompose/solve it