The Kurutto Corporation has three factories producing child strollers for shipment to four distribution centers. The monthly production of plants $1,2,$ and $3$ is $12,16,$ and $10$ shipments, respectively. Every distribution center must receive $10$ shipments each month. Unmet demand will incur a $$100$ per shipment penalty. The cost of shipping from each plant to its respective distribution center is detailed in the table below.

Table $2$: Shipment cost between plants and Distribution Centers

$\backslash$table$[[,$DC$1,$DC$2,$DC$3,$DC$4],[$Plant $1,$$$80,$$$90,$$$40,$$$60$