The city of Squaretown wants to build a recreation center for senior citizens who live in three ...

     The city of Squaretown wants to build a recreation center for   senior citizens who live in three low-income apartment buildings (A, B, and   C). Squaretown is a town with only horizontal and vertical streets and so   each city block is a perfect square. Each unit represents one city block. The   table below provides the map coordinates of each apartment building and the   number of senior citizens in each building:   Apartment building Map coordinates    (x, y)   A (1, 2)   B (3, 8)   C (7, 5)   Squaretown   believes that the best location for the senior citizens center is the one   that minimizes the sum of the products obtained by multiplying each apartment   building’s senior citizen population by the building’s distance from the   center (as measured by the number of city blocks). For example, if the center   were built at map coordinates (4, 5), the sum of products would be                                  100 (|4 – 1|+|5 – 2|) + 300 (|4 – 3| + |5 – 8|) + 200 (|4 – 7| + |5 – 5|)   =2400   Formulate a   goal programming model that Squaretown can use to determine where to locate   the senior citizens center. Give the mathematical (algebraic) model by   defining the decision variables, deviation variables, constraints plus   objective function. Set up a spreadsheet model and solve it using the Excel   Solver to find the optimal solution. What is the optimal location for this   center?