TN Communications provides cellular telephone services. The company is planning to expand into the Cincinnati area and is trying to determine the best location for its transmission tower. The tower transmits over a radius of 10 miles. The locations that must be reached by this tower are shown in the following figure.

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TN Communications would like to find the tower location that reaches each of these cities and minimizes the sum of the distances to all locations from the new tower.

a. Formulate and solve a model to find the optimal location.

b. Formulate and solve a model that minimizes the maximum distance from the transmission tower location to the city locations.