LP$\mathrm{.}07$ Tri$-$State Manufacturing has three factories $(1,2,$ and $3)$ and three warehouses $($A$,$ B$,$ and C$).$ The following table shows the shipping costs between each factory and warehouse, the factory manufacturing capabilities $($in thousands$),$ and the warehouse capacities $($in thousands$).$ Management would like to keep the warehouses filled to at least their capacity in order to generate demand.

Warehouse A Warehouse B Warehouse C Production Capability

Factory $16\mathrm{.}005\mathrm{.}003\mathrm{.}006$

Factory $28\mathrm{.}0010\mathrm{.}008\mathrm{.}008$

Factory $311\mathrm{.}0014\mathrm{.}0018\mathrm{.}0010$

Capacity $7125$

What is the lowest possible shipping cost?

Preview $($round to the nearest whole number$)$

How much inventory will be shipped from factory $2$ to warehouse B$?$

Preview $($round to the nearest whole number$)$

How much inventory will be shipped from factory $3$ to warehouse B$?$

Preview $($round to the nearest whole number$)$

How much inventory will be shipped from factory $2$ to warehouse A$?$

Preview $($round to the nearest whole number$)$