2. (10 points) Consider the three-floor building in which there are eight offices. The manager of the building wants to find a suitable location for a mail distribution room used collectively by all the offices. The existing offices are located at the points P * 1 = (15, 25, - 8) P_{2} = (40.2 * 0.2) P * 3 = (8, 20, 2) P * 4 = (30, 40, 2) P_{5} = (25.35 * 0.12) , P_{6} = (25, 35, 12) P * 7 = (25, 35, 22) and P * 8 = (12, 10, 22) Office 1 is on the ground floor. Office 2, Office 3, and Office 4 are on the 1st floor. Office 5 and Office 6 are on the 2nd floor, and finally, Office 7 and Office 8 are on the 3rd floor.

a) The weights for the existing offices are 1, 2, 2, 3, 1, 2, 2, and 1. Assuming rectilinear distance is a reasonable approximation of the actual travel distance, what is the location of the mail distribution room which will minimize the total distance that the people working in these offices have to travel? (5 points)

b) Assume now that all the weights are equal. Assume that the coordinates of the mail distribution room; x = 20 y = 25 determine which floor is optimal for that mail

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distribution room that will minimize the total distance that the people working in these offices have to travel. (5 points)