Bath tubes are produced in three different plants: Des Moines $($D$),$ Evansville $($E$)$ and Fort Lauder $($F$).$ The tubes are shipped to three different cities: Albuquerque $($A$),$ Boston $($B$)$ and Cleveland $($C$).$ Each plant is able to supply the following number of units: Des Moines $100$ units, Evansville $300$ units and Fort Lauder $300$ units. The demands of each city are as follows: Albuquerque $300$ units, Boston $200$ units and Cleveland $200$ units. How many units of bath tubes must D$,$ E and F transport to cities A$,$ B and C so that the the total shipping costs is at its minimum? What is the minimum total cost?