(2-Center on a Tree) Prove that Algorithm 8.11 finds the optimal solution to the absolute 2-center..

(2-Center on a Tree) Prove that Algorithm 8.11 finds the optimal solution to the absolute 2-center problem. (N-Echelon Location Problem) By extending the approach used in Section 8.7.1, formulate a facility location model with N echelons, for general N = 3. Echelon N ships products to echelon N - 1, which ships products to echelon N - 2, and so on; echelon 1 serves the end customer. The locations of the facilities in echelons 2, . . . , N are to be decided by the model, and there are fixed costs for each. Define any new notation clearly. Explain the objective function and each of the constraints in words. Note: No decision variables should have more than 3 indices.