Kiddie Clothes wishes to locate its warehouse so that it would serve its four different stores, described as follows. Based on the center of gravity, what are the x and y coordinates of the proposed warehouse location?
A) x is less than or equal to 3; y is less than or equal to 2.
B) x is less than or equal to 3; y is less than or equal to 2.5.
C) x is greater than or equal to 2.5; y is greater than or equal to 3.
D) x is less than or equal to 2.5; y is greater than or equal to 2.9.

Question

Kiddie Clothes wishes to locate its warehouse so that it would serve its four different stores, described as follows. Based on the center of gravity, what are the x and y coordinates of the proposed warehouse location? 
A) x is less than or equal to 3; y is less than or equal to 2. 
B) x is less than or equal to 3; y is less than or equal to 2.5. 
C) x is greater than or equal to 2.5; y is greater than or equal to 3. 
D) x is less than or equal to 2.5; y is greater than or equal to 2.9.

Quizplus · Accepted Answer

To find the center of gravity, we need to calculate the weight of each store (the number of units sold multiplied by the distance from the origin) and then divide by the total weight. Using the given data, we can calculate the weights and distances as follows:

Store A: (1000 * sqrt(13)) = 3605.6
Store B: (900 * 1) = 900
Store C: (1200 * sqrt(5)) = 3394.4
Store D: (800 * sqrt(34)) = 3727.6

Total weight = 3900
X coordinate = (3605.6 + 900 + 3394.4 + 3727.6) / 3900 = 2.81
Y coordinate = (1000 * sqrt(13) * 2 + 900 * 4 + 1200 * sqrt(5) * 1 + 800 * sqrt(34) * 3) / 3900 = 2.93

Therefore, the best choice is D, which states that the x coordinate is less than or equal to 2.5 and the y coordinate is greater than or equal to 2.9.

Kiddie Clothes Wishes to Locate Its Warehouse So That It