Question: 1. A machine shop has five machines, located at (3, 3), (3, 7), (8, 4), (12, 3), and (14, 6), respectively. A new machine is

1. A machine shop has five machines, located at (3, 3), (3, 7), (8, 4), (12, 3), and (14, 6), respectively. A new machine is to be located in the shop with the following expected numbers of loads per hour transported to the existing machines: 1/8, 1/8, 1/4, 1, and 1/6. Material is transported along parallel aisles, so a rectilinear distance measure is appropriate.

a) Find the coordinates of the optimal location of the new machine to minimize the weighted sum of the squared straight-line distances from the new machine to the existing machines.

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