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1. The county is considering building one facility.

A. Formulate the model as a non-linear programming model to answer the following questions. Provide the model and all of the constraints (if necessary).

B. Where should the county locate the facility in order to minimize the total distance traveled in one year? (XY coordinates)

C. What is the total distance traveled in one year?

D. Draw a map with the location of each town and the location of the facility. (Use scatter plot in MS Excel or Open Office to draw the map use Excel template provided).

E. What is the average one-way distance for each trip? (Remember average distance is total distance divided by total number of trips)

2. The county is considering building two facilities.

A. Formulate the model as a binary integer non-linear programming model. Provide the model and all of the constraints (if necessary).

B. Where should each of the two facilities be located in order to minimize the total distance traveled each year? (XY coordinates)

C. Assume trips will be made to each town from only one facility. What is the total distance traveled in one year?

D. Draw a map with the location of each town and the location of the two facilities. (Use scatter plot in MS Excel or Open Office to draw the map).

E. What is the average one-way distance for each trip?

3. The county is considering building three facilities.

A. Formulate the model as a binary integer non-linear programming model. Provide the model and all of the constraints (if necessary).

B. Where should each of the three facilities be located in order to minimize the total distance traveled each year?

C. Assume trips will be made to each town from only one facility. What is the total distance traveled in one year?

D. Draw a map with the location of each town and the location of the three facilities. (Use scatter plot in MS Excel or Open Office to draw the map).

E. What is the average one-way distance for each trip?Note: this is problem 5 from the attached file

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