The maximal flow problem (or max flow problem) is a type of network flow problem in which the goal is to determine the maximum amount of flow that can occur in the network. In a maximal flow problem, the amount of flow that can occur over each arc is limited by some capacity restriction. This type of network might be used to model the flow of oil in a pipeline (in which the amount of oil that can flow through a pipe in a unit of time is limited by the diameter of the pipe). Traffic engineers also use this type of network to determine the maximum number of cars that can travel through a collection of streets with different capacities imposed by the number of lanes in the streets and speed limits. The Fargo Oil Company operates an oil field and a refinery in North Dakota. The crude obtained from the oil field is pumped through the network of pumping substations, as shown in the figure. Pumping Station 1 Pumping Station 3 Oil Field Refinery o Refinery 0-0 Pumping Station 2 Pumping Station 4 The amount of oil that can flow through each of the pipelines, represented by the arcs in the network, varies due to differing pipe diameters. The numbers next to the arcs in the network indicate the maximum amount of oil that can flow through the various pipelines (measured in barrels of oil per second). The Fargo Oil Company wants to determine the maximum number of barrels of oil per second that can flow from the oil filed to 1200 miles away refinery. A) Create an LP model in order to help company to determine the maximum number of barrels of oil per second that can flow from the oil filed to 1200 miles away refinery. Hint: Clearly describe decision variables for full credit. B) Solve your model using either LINDO or Excel Solver. Clearly explain the model solution by listing amount of flow on each pipeline on the network