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$($A transportation problem$)$ There are three warehouses at different cities: Detroit, Pittsburgh and Buffalo. They have $250,130$ and $235$ tons of paper accordingly. There are four publishers in Boston, New York, Chicago and Indianapolis. They ordered $75,230,240$ and $70$ tons of paper to publish new books. The costs of transportation for one ton of paper are listed as follows:

From $\backslash \backslash$ To Boston $($BS$)$

New York $($NY$)$

Chicago $($CH$)$

Indianapolis $($IN$)$

Detroit $($DT$)15201621$

Pittsburgh $($PT$)$

$2513511$ Buffalo $($BF$)1515717$

Please find the optimal plan of transportation that satisfies all orders and minimizes the total transportation cost $(10$ pts$).$