Widgeco, a manufacturing company specializing in Widgets, has three Factories. Factory $1$ is on the East coast, Factory $2$ is in the Midwest and Factory $3$ is on the West coast. Widgeco sells to three distributors who purchase Widgets exclusively from Widgeco. Distributor $1$ is on the East coast, Distributor $2$ is in the Midwest and Distributor $3$ is on the West coast. Each Widgeco factory has a maxiumum monthly production capacity. Factory $1$ can produce $1000$ Widgets each month, Factory $2$ can produce $3000$ Widgets each month and Factory $3$ can produce $4000$ Widgets each month. Distributors $1,2,$ and $3$ require $2500,2000,$ and $3500$ Widgets each month, respectively. Each Widgeco factory can produce a Widget for the same price, but shipping prices vary based on the location of the distributor $($see the table below$).$ Widgeco wants to figure out a shipping plan that will minimize total cost while satisfying the distributor demand.

Shipping Cost Per Widget Distributor $1$

$($East Coast$)$ Distributor $2$

$($Midwest$)$ Distributor $3$

$($West Coast$)$

Factory $1($East coast$)$ $$14$ $$24$ $$32$

Factory $2($Midwest$)$ $$22$ $$13$ $$26$

Factory $3($West coast$)$ $$36$ $$27$ $$17$