A national firm has beef jerky processing facilities in Locations $1,2,3,$ and $4.$ They ship to central distributors $($represented as A$,$ B$,$ C$,$ and D$)$ handling four regions of the country. The per$-$unit shipping costs between each possible combination of locations are shown in the following table.

A

B

C

D

$1$

$$5$

$$10$

$$5$

$$4$

$2$

$$3$

$$4$

$$4$

$$3$

$3$

$$8$

$$6$

$$8$

$$2$

$4$

$$2$

$$3$

$$5$

$$9$

The processing facility locations are capable of monthly production $($in tons$)$ as follows:

Location $1$: $600$

Location $2$: $350$

Location $3$: $475$

Location $4$: $850$

The central distributors have firm commitments for the following quantities:

Distributor A: $650$

Distributor B: $725$

Distributor C: $400$

Distributor D: $500$

What is the lowest$-$cost shipping arrangement that can be made between the plant locations and distributors and what is the annual shipping cost?