Two plants are to serve three market points through one warehouse, as shown in the figure below. Volume flowing either to or from each point, and the associated transportation rates, are given as follows:

Point No$.$ Point, i Volume, Vi Transportation Rate, Ri $($$$/$cwt$./$mi$.)$

$1$ P$15,0000\mathrm{.}095$

$2$ P$26,0000\mathrm{.}095$

$3$ M$16,5000\mathrm{.}04$

$4$ M$24,0000\mathrm{.}04$

$5$ M$34,5000\mathrm{.}095$

Please first use both the center$-$of$-$gravity method to find the approximate location for a single warehouse location. Then, use exact center$-$of$-$gravity method $($COG module$)$ to find the optimum single warehouse location.