Question

Elyria Warehousing desired to locate a central warehouse to serve five Ohio markets. Placed on a grid system, its five markets had coordinates and demand as shown below.

Location Coordinates (miles)

Demand (units)

(45, 65)

2,200

(120, 55)

900

(160, 95)

1,300

(100, 200)

1,750

(195, 175)

3,100



Calculate the Y-coordinate of the center-of-gravity location using the center-of-gravity technique.

69 miles
131 miles
53 miles
197 miles
171 miles

Answer 1

Answer:

The correct option is 2.

Step-by-step explanation:

According to the the center-of-gravity technique, the coordinates of the center-of-gravity location are

$(\frac{\sum x_iL_i}{\sum L_i},\frac{\sum y_iL_i}{\sum L_i})$

Where ($(x_i,y_i)$ represent the coordinates and $L_i$ is demand.

We have to find the Y-coordinate of the center-of-gravity location.

The sum of product of demand and corresponding y coordinates is

$\sum y_iL_i=65\times 2200+55\times 900+95\times 1300+200\times 1750+175\times 3100=1208500$

The sum of demanded units is

$\sum L_i=2200+900+1300+1750+3100=9250$

The Y-coordinate of the center-of-gravity location is

$y_0=\frac{\sum y_iL_i}{\sum L_i}$

$y_0=\frac{1208500}{9250}$

$y_0=130.6486$

$y_0\approx 131$

The Y-coordinate of the center-of-gravity location is 131. Therefore the correct option is 2.