A European bookstore chain wants to enter the US market by opening various outlets in NY City. To this end, 9 potential locations have been identified. However, some of these locations are very close to others, and the management wants the outlets to be separated within a certain distance so they do not compete for the same clients. Below is a table with the 9 geographical locations considered (a to i) and the locations that conflict with them due to their proximity. The goal is to set up as many outlets as possible while fulfilling the distance policy. a) Formulate an optimization model (decision variables, objective function, and constraints) that optimally chooses how many outlets to set up and where (write it in the booklet) b) Solve the model using Lingo. c) Write and explain your result in the booklet. A European bookstore chain wants to enter the US market by opening various outlets in NY City. To this end, 9 potential locations have been identified. However, some of these locations are very close to others, and the management wants the outlets to be separated within a certain distance so they do not compete for the same clients. Below is a table with the 9 geographical locations considered (a to i) and the locations that conflict with them due to their proximity. The goal is to set up as many outlets as possible while fulfilling the distance policy. a) Formulate an optimization model (decision variables, objective function, and constraints) that optimally chooses how many outlets to set up and where (write it in the booklet) b) Solve the model using Lingo. c) Write and explain your result in the booklet