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A larger and more modern main post office is to be constructed at a new location

ID: 378378 • Letter: A

Question

A larger and more modern main post office is to be constructed at a new location in Davis, California. Growing suburbs caused a shift in the population density from where it was 40 years ago, when the current facility was built. Annette Werk, the postmaster, asked her assistants to draw a grid map of the seven points where mail is picked up and delivered in bulk. The coordinates and trips per day to and from the seven mail source points and the current main post office, M, are shown in the following table. M will continue to act as a mail source point after relocation.

  

Mail Source Point

Round trips per day

x, y, Coordinates (miles)

1

7

(15,4)

2

6

(2,12)

3

1

(17,10)

4

16

(2,9)

5

7

(3,6)

6

1

(5,11)

7

8

(7,17)

M

7

(1,4)

a. Calculate the center of gravity as a possible location for the new facility. (Enter your responses rounded to the nearest whole number.)

The center of gravity "X" coordinate = ______

The center of gravity "Y" coordinate = ______

Enter your answer in the edit fields and then click Check Answer.

Mail Source Point

Round trips per day

x, y, Coordinates (miles)

1

7

(15,4)

2

6

(2,12)

3

1

(17,10)

4

16

(2,9)

5

7

(3,6)

6

1

(5,11)

7

8

(7,17)

M

7

(1,4)

Explanation / Answer

By C.G. method

Cx = X1V1 +X2V2+.....+XnVn / V1+V2 +...Vn

Cy = Y1V1+Y2V2+....+YnVn / V1+V2+...Vn

Cx = 15x7+2x6+17x1+2x16+3x7+5x1+7x8+1x7 /53

= 4.81

Cy = 4x7+12x6+10x1+9x16+6x7+11x1+17x8+4x7 /53

= 471/53 =8.88

Hence the point is (4.81,8.88)

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