Question

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?

Answer

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