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Linear Operators - QM Software Format

14. Your company buys and sells fresh catfish, utilizing containerized chill boxes. Each box is carried by airfreight to either of two airfreight hubs, where it is further routed to restaurant wholesalers in various cities. Once loaded with fish, containers may be held at origin for further shipment for up to three days until orders are received. Minimizing cost of transportation is one of the keys to maintaining an operating profit margin.
The possible transshipment hubs are Birmingham, AL or Atlanta, GA.
Today you have available 3 containers in Slidell, La., 6 containers in Greenville, Mississippi, and 5 containers in Dothan, Alabama. You have sales for today of 2 containers in Macon, Georgia, 4 containers in Greenville, South Carolina, and 3 each in Jacksonville, Florida and Savannah, Georgia.

Airfreight shipping charges, per pound, in cents, for the class and size of your containers is as shown in the table below.

from/to Birmingham Atlanta

Slidell 8 6
Greenwood 3 8
Dothan 9 3
Macon 44 57
Greenville 35 34
Jacksonville 34 28
Savannah 24 32

a. Determine the optimum routing that will minimize shipping costs and satisfy demand.
b. Where, if at all, will containers have to be held and how many at each site?

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