A startup company decided to enter to deliver lumber to customers in their region every

week. They identified five potential customers $($PC$1,$ PC$2,$ PC$3,$ PC$4,$ and PC$5)$ and three

potential sites for installing its warehouses $($W$1,$ W$2,$ and W$3).$ They have to provide $80,270,$

$250,160,$ and $180$ tons of lumber per week to PC$1,$ PC$2,$ PC$3,$ PC$4,$ and PC$5,$ respectively. Each

warehouse costs about $$1000$ per week, including the rent and maintenance, independent of

the volume it services. This volume is limited to $500$ tons, the maximum amount that may be

handled weekly.