An operations manager wants to use gravity location approximation to decide the location of a warehouse. The x and y coordinates of three customer locations, demand $($D$)$ at those locations, and transportation costs per unit per mile $($F$)$ are presented in the table below. Help the operations manager by finding the approximate location of the warehouse.

Customers

x

y

F

D

$1$

$10$

$20$

$1$

$10$

$2$

$20$

$5$

$1$

$20$

$3$

$10$

$10$

$2$

$10$

Group of answer choices

x$=14,$ y$=10$

x$=10,$ y$=15$

x$=20,$ y$=10$

x$=10,$ y$=14$

x$=13\mathrm{.}3,$ y$=11\mathrm{.}7$