Assignment:
A rural district is planning the location of its fire station. The station will have to serve seven villages. The coordinates of the villages are (0, 0), (6, 1), (2, 3), (8, 3), (0, 4), (4, 5), and (3, 7). As the people in the district are fierce defenders of property rights, the roads were constructed parallel to the rectangular fields.
(a) What is the optimal minimax location of the fire station?
(b) Suppose that it takes the fire truck and its crew 3 min to get ready after an emergency call, 2 min to drive one distance unit, and another 3 min to get the hoses and pumps going. Given the solution determined under(a), how much time elapses between the phone call and the beginning of the fire fighting action at the site of the most distant customer? How long does it take on average?
Provide complete and step by step solution for the question and show calculations and use formulas.