The Hamilton County Local Government has eight sectors which need fire protection. Adequate Fire protection can be provided in each sector either by building a fire station in that sector, or by  building a fire station in another sector which is no more than a 12-minute drive away. The time to drive between the centers of each pair of sectors is given in the following table. (Because of one-way streets and left turns the times are not symmetric.) The cost to build a fire station is the  same in each sector.              Formulate an integer programming model to choose which sectors should have their own fire station.   Solve the model by using Excel Solver.

The director of Burtonsville Civil Defense Agency has been ordered to draw up a disaster plan for assigning casualties to hospitals in the event of a serious earthquake. For simplicity, we will assume that causalities will occur at two points in the city and will be transported to three hospitals. It is estimated that there will be 300 casualties at point A and 200 at point B. Travel times to hospitals 1, 2, and 3 are 25, 15, and 10 minutes, respectively; from point B they are 20, 5, and 15 minutes. Hospital capacities for emergency cases are 250, 150, and 150 patients. How should the victims be assigned to hospitals to minimize the total time lost in transporting them?     Disaster Point Hospital Total Casualties 1 2 3 A 25   15   10   300 B 20   5   15   200 Maximum Capacity 250   150   150     Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You…

The distance between two cities in the United States can be approximated by the following formula, where lat1 and long1 are the latitude and longitude of city 1 and lat2 and long2 are the latitude and longitude of city 2. 69   (lat1 − lat2)2 + (long1 − long2)2 Ted's daughter is getting married, and he is inviting relatives from 15 different locations in the United States. The file Wedding gives the longitude, latitude, and number of relatives in each of the 15 locations.   Ted would like to find a wedding location that minimizes the demand-weighted distance, where demand is the number of relatives at each location. Assuming that the wedding can occur anywhere, find the latitude and longitude of the optimal location. (Hint: Notice that all longitude values given for this problem are negative. Make sure that you do not check the option for Make Unconstrained Variables Non-Negative in Solver. Round your answers to three decimal places.) latitude of the optimal wedding location:…