A chemical processing plant has a network of pipes that are used to transfer liquid chemicalproducts from one part of the plant to another. The numbers next to the arcs in the network indicatethe maximum amount of chemicals that can flow through the various pipelines (measured in barrelsper minute). Formulate a LP model that will maximize flow to location 7 from location

Explanationis the long-distance transportation of a liquid or gas through a system of pipes—a pipeline—typically to a market area for consumption. The latest data from 2014 gives a total of slightly less than 2,175,000 miles (3,500,000 km) of pipeline in 120 countries of the world.[1] The United States had 65%, Russia had 8%, and Canada had 3%, thus 75% of all pipeline were in these three countries.[1]

Pipeline and Gas Journal's worldwide survey figures indicate that 118,623 miles (190,905 km) of pipelines are planned and under construction. Of these, 88,976 miles (143,193 km) represent projects in the planning and design phase; 29,647 miles (47,712 km) reflect pipelines in various stages of construction. Liquids and gases are transported in pipelines and any chemically stable substance can be sent through a pipeline.[2] Pipelines exist for the transport of crude and refined petroleum, fuels – such as oil, natural gas and biofuels – and other fluids including sewage, slurry, water, beer, hot water or steam for shorter distances. Pipelines are useful for transporting water for drinking or irrigation over long distances when it needs to move over hills, or where canals or channels are poor choices due to considerations of evaporation, pollution, or environmental impact.: