Question: (25 points) Consider points in the 2-dimensional plane (i.e., (x,y) ). For any two points (x1,y1) and (x2,y2) in a 2D plane, we define their

(25 points) Consider points in the 2-dimensional

(25 points) Consider points in the 2-dimensional plane (i.e., (x,y) ). For any two points (x1,y1) and (x2,y2) in a 2D plane, we define their 1-distance 1 to be x1x2+y1y2. Intuitively, the 1-distance is the distance between two points if one can only go horizontally or vertically, not diagonally. Washtenaw County has decided to build a new high school in 2023 to serve three towns: Town 1, Town 2 and Town 3. The county must decide where to build the new school. The new school can be built anywhere, and Towns 1,2 and 3 are located at points (0,0),(1,10),(9,6), respectively. The county wants to place the school such that the maximum distance between the towns and the school is minimized. Formulate a linear program to find the optimal location of the post office. You do not need to use generic form, please write all parts of the linear program in specific form. (Note: the objective function and all constraints must be linear.)

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