what is the lowest cost solution while satisfying the constraints

You work for a large intermodal carrier and are in charge of repositioning empty containers each week. Intermodal ramps are imbalanced - in some cities, more containers flow in than out, and in others more containers flow out than in. You need to develop a plan to reposition the empty containers. Locations with negative values have too many containers, which need to flow out (for example, at most 200 containers can flow out of SLC). Locations with positive values do not have enough containers, which need containers to flow in (for example, at least 300 containers need to flow into CHI). Costs for sending a container between each city pair is shown on the graphic. Formulate this as a network flow model and solve it. What is the lowest cost solution while satisfying the constraints? This spreadsheet might help you think through the problem Container Network Balance.xlsx . ORIGINSLCSLCSLCDENOENDENPHOPHOPITPITPITPITATLATLATLATLMLADESTINATIONSEACHILACHILADALLADALNYCDETCHIINDDALINDNYCSAVSAVCOST$$$$$$$$$$$$$$$$$250400300400250200150300300250200100250250400200100FLOW SOURCESSLCDENPHOPITATLMIASINKSSEALACHIDETINODALNYCSAVMAXCONSTRAINTUSED20010020030025050MINCONSTRAINTUSED501003001005010015050