Part 1: Rockhill Shipping & Transport Company 

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

Allen has estimated the cost of shipping a barrel of waste from each of the six plants to each of the three waste disposal sites as shown in the following table. 

The plants generate the following amounts of waste products each week:

The three waste disposal sites at Orangeburg, Florence, and Macon can respectively accommodate a maximum of 65, 80, and 105 barrels per week. 

In addition to shipping directly from each of the six plants to one of the three waste disposal sites, Allen is also considering using each of the plants and the waste disposal sites as intermediate shipping points. In this case, trucks would be able to drop a load at a plant or a disposal site to be picked up and carried on to the final destination by another truck. Furthermore, Rockhill would not incur any handling costs because Chimitoxic has agreed to take care of all the handling costs at the plants and at the disposal sites. In other words, Rockhill’s only cost will be the transportation cost. Therefore, Allen wants to be able to consider the possibility that it may be cheaper to drop and pick up loads at intermediate points rather than ship them directly.  

Allen has estimated the shipping costs per barrel between each of the six plants to be as follows: 

The estimated shipping cost per barrel between each of the waste disposal sites is as follows:

Allen wants to determine the shipping routes that will minimize Rockhill’s total cost in order to develop a contract proposal to submit to Chimotoxic for waste proposal. He particularly wants to know if it would be cheaper to ship directly prom the plants to the waste sites or if he should drop and pick up some loads at the various plants and waste sites.  

In the word document, explain the details of the solutions obtained for the optimal routes and their respective optimal costs for both cases. In particular for the case when loads are dropped and picked up at various plants and waste sites, explain how many barrels, in total, will be transported each week from a source to a destination.