Math

Rachel Sundusky is the manager of the South-Atlantic office of the Stateline Shipping and Transport Company. She is in the process of negotiating a new shipping contract with Polychem, a company that manufactures chemicals for industrial use. Polychem wants Stateline to pick up and transport waste products from its six plants to three waste disposal sites. Rachel is very concerned about this proposal arrangement. The chemical wastes that will be hauled can be hazardous to humans and the environment if they leak. In addition, a number of towns and communities in the region where the plants are located prohibit hazardous materials from being shipped through their municipal limits. Thus, not only will the shipments have to be handled carefully and transported at reduced speeds, they will also have to traverse circuitous routes in many cases.

Rachel has estimated the cost of shipping a barrel of waste from each of the six plants to each of the waste disposal sites as shown in table 1 below:

Waste Disposal Site

Plant Whitewater Los Canos Duras

Kingsport $12 $15 $17

Danville $14 $9 $10

Macon $13 $20 $11

Selma $17 $16 $19

Columbus $7 $14 $12

Allentown $22 $16 $18

Table 2 below shows the plants generate the following amounts of waste products each week.

Plant Wast/Wk

Kingsport 35

Danville 26

Macon 42

Selma 53

Columbus 29

Allentown 38

The three waste disposal sites at Whitewater, Los Canos, and Duras can accommodate a maximum of 65, 80, and 105 barrels per week, respectively as shown in table 3 below:

Site Capacity

Whitewater 65

Los Canos 80

Duras 105

In addition to shipping directly from each of the six plants to one of the three waste disposal sites, Rachel is also considering using each of the plants and waste disposal sites as intermediate shipping points. Trucks would be able to drop a load at a plant or disposal site to be picked up and carried on to the final destination by another truck, and vice versa. Stateline would...