OPTIMIZATION PROBLEM:

2. The figure below represents a gas distribution network. The numbers on arcs indicate the capacities of the corresponding pipes. 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)