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Question

Weight Location A Location B Location C
Wages 40 30 75 90
Labor Climate 30 40 70 40
Taxes 15 80 40 90
Utilities 15 75 60 10
Total 100
Weighted sum 4725 6600 6300
Weighted average 47.25 66 63

16) A contractor for the military is looking for a new location for a supply depot. The depot will supply four bases whose tonnage (demand) and map coordinates are shown below. If management wants the depot to have a central location, what should be its map coordinates?


Bases (X,Y) Coordinates Tonnage
Fort Able (40,110) 30,000
Base Baker (70,50) 60,000
Camp Charlie (90,20) 35,000
Camp Delta (70,80) 75,000

Answer: The depot should be located near X = 69, Y = 65.


Bases Weight X coord Y coord X mult. Y mult.
Fort Able 30,000 40 110 1,200,000 3,300,000
Base Baker 60,000 70 50 4,200,000 3,000,000
Camp Charlie 35,000 90 20 3,150,000 700,000
Camp Delta 75,000 70 80 5,250,000 6,000,000
Sum 200,000 270 260 13,800,000 13,000,000
Weighted Average 69 65

17) A highway contractor needs to locate a single supply point to provide road building materials to four projects. The four projects, which are all approximately the same magnitude, are located at the following coordinates. Coordinate units are in miles.


X (East) Y (North)
Project A 50 10
Project B 15 60
Project C 40 60
Project D 30 20

a. On the grid below, plot the locations of the four road-building sites. Properly label all points.

b. What is the center of gravity?

c. If a single truck were sent from center-of-gravity to each project and back (four round trips), how many miles would be traveled? (Hint: use the Pythagorean Theorem C =).

d. Add the calculated center of gravity to the grid.

Answer:

a. Coordinates are (50, 10), (15, 60), (40,60), and (30, 20)

b. The supply point should be at (33.75, 37.50).

Answer

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