Question

Mega-Mart, a discount store chain, wants to build a new superstore in an area in southwest Virginia near four small towns with populations between 8000 and 42,000. The coordinates (in miles) of these four towns and the market population in each are as follows:

Whitesburg Altonville Camburg Milligan
x=12 x=18 x=30 x=32
y=20 y=15 y=7 y=25
w=26,000 w=12,000 w=18,300 w=9,700


Determine the best site using the center-of-gravity technique.

Answer 1

The center-of-gravity technique can be used to determine the best site for a new store by calculating the weighted average of the coordinates of the towns. The best site for Mega-Mart's new superstore in southwest Virginia is at coordinates (18.545, 16.833).

Step-by-step explanation:

The center-of-gravity technique can be used to determine the best site for Mega-Mart's new superstore. The center of gravity is calculated by finding the weighted average of the coordinates of the towns, where the weights are the market populations. Here are the steps to determine the best site:

1. Calculate the sum of the market populations: 26,000 + 12,000 + 18,300 + 9,700 = 66,000.
2. Calculate the weighted average x-coordinate: (12 * 26,000 + 18 * 12,000 + 30 * 18,300 + 32 * 9,700) / 66,000 = 18.545 miles.
3. Calculate the weighted average y-coordinate: (20 * 26,000 + 15 * 12,000 + 7 * 18,300 + 25 * 9,700) / 66,000 = 16.833 miles.
4. The best site for the new superstore is at coordinates (18.545, 16.833).