Use half sum method
Let four existing facilities be located at P₁ = (0, 10). P₂=(5, 10), P₃=(5, 15), and P₄= (10,5) with w₁=15, w₂= 20, w₃=35, and w₄=30. Determine the optimum location for a single new facility when cost is proportional to rectilinear distance. Construct a contour line passing through the point having coordinates (10, 10).