Lucy has just finished her studies and decides to start her own account in the field of acericulture. It therefore acquired 9 plots of land, in the West region, where it wishes to develop its activity. The acericulture process requires the collection of maple sap which is then transported, through pipes, to the sugar shacks where it will be processed into maple syrup. Given the geolocation of the different plots, it is impossible to interconnect them all of them have one sugar shack. Lucy therefore identified 6 potential sites where she could build its sugar shacks with different processing capacities. Table 1 shows the possibilities for Lucy to connect, through the pipes, the Maple trees from each plot of land to each potential sugar shack site. This painting also gives the amount of maple syrup that can be processed at each potential site sugar shack, as well as the total distance that the maple sap will have to travel to cabins. Note that the longer this distance, the more the maintenance cost of these pipes. raised. Lucy wants to make sure that each of her plots is connected to at least one sugar shack. And taking into account the municipal regulations, it is not possible to build sugar shacks at both sites 5 and 6. Also, at sites 1, 3 and 4, we cannot have more of 2 sugar shacks. In addition, Madame Blais' restricted budget cannot allow her to build more than three sugar shacks, and also buy more than 100km of piping. Propose an optimization model to Lucy that will allow her to maximize the productivity of its activity by respecting all the restrictions which are presented to it. Clearly identify the decision-making variables, the objective function and the constraints of the model.

Plots Site 1 Site a Site 3 Site 4 Site site 5 Site 6 1 3 3 4 J V u s 7 } 8 LO D v Productivity 1235 345 4.25 300 325 450 (im gellon) Distance (km) 30 35 40 2 o 30 st