The figure below represents a gas distribution network. The numbers on arcs indicate the capacities of the corresponding pipes. A 5 8 2 5 3 8 5 5 2 3 6 B Suppose that the construction of a new pipeline from node A to node 4 is considered. If the pipeline (A,4) is constructed, then its capacity will be 3, and the capacity of the pipeline (A,3) will have to be reduced to 6. Formulate a mathematical model to determine whether the new pipeline should be constructed to maximize the amount of gas that can be sent from A to B. (Define decision variables, write each constraint and the objective function clearly).