A company in P$.$O$.$L manufactures in three plants, referred to as P$1,$ P$2,$ and P$3.$ The company ships its products from plants to two central distribution centers $($DCs$),$ designated D$1$ and D$2,$ and then to five regional warehouses, W$1$W$5.$

Each distribution center has a capacity to flow through, which is $100$ tons per day.