The Rugger Corporation is a Seattle-based R&D company that recently developed a new type of fiber substrate that is waterproof and resists dirt. Several carpet manufacturers in northeast Georgia want to use Rugger as their sole supplier for this new fiber. The locations of the carpet manufacturers are summarized in the following table:

Carpet Mill Locations X-Coordinate Y-Coordinate

Dalton 9 43

Rome 2 28

Canton 51 36

Kennesaw 19 4

Rugger expects to make 130, 75, 90, and 80 deliveries to the carpet producers in Dalton, Rome, Canton, and Kennesaw, respectively. The company wants to build its new plant in a location that would minimize the annual shipping miles. However, Rugger also wants to be within 50 miles of each of the new customers so that it will be easy to provide on-site technical support for any production problems that may occur.

a. Formulate an NLP model for this problem. b. Implement your model in a spreadsheet and solve it. e. Suppose the company wants to identify the location that minimizes maximum distance to any of its customers. Where is this location and how many annual shipping miles would Rugger incur if the new plant is located there?

For problem 27e, you will not multiply 130, 75, 90, and 80 by Distances. use excel pictures.