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. What is the center of gravity?
b. 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 = ).
a. The supply point should be at (33.75, 37.50 ).
Weight X coord Y coord
Project A 1 50 10
Project B 1 15 60
Project C 1 40 60
Project D 1 30 20
Sum 4 135 150
Average 33.75 37.5
Weighted Average 33.75 37.5
b.
Distance to COG
Project A 31.94
Project B 29.29
Project C 23.35
Project D 17.90
31.94(2 ) + 29.29(2 ) + 23.35(2 ) + 17.9(2 ) = 204.96 total miles traveled
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