$3.(40$ points$)$ Using the continuous multi$-$facility rectilinear minisum heuristic $($location$-$allocation$)$ we learned in class, find the optimal location of two facilities, given the following data:

$\backslash$begin$\{$tabular$\}\{|$l$|$r$|$r$|$r$|\}$

$\backslash$hline Customer & $\backslash$begin$\{$tabular$\}\{$r$\}$

x$-$coor. $\backslash \backslash$

$($miles$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$r$\}$

y$-$coor. $\backslash \backslash$

$($miles$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$r$\}$

Demand $\backslash \backslash$

$($units$/$day$)$

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline A & $1$ & $30$ & $12\backslash \backslash$

$\backslash$hline B & $30$ & $25$ & $4\backslash \backslash$

$\backslash$hline C & $3$ & $2$ & $5\backslash \backslash$

$\backslash$hline D & $27$ & $38$ & $5\backslash \backslash$

$\backslash$hline E & $35$ & $23$ & $7\backslash \backslash$

$\backslash$hline F & $45$ & $1$ & $4\backslash \backslash$

$\backslash$hline G & $19$ & $35$ & $11\backslash \backslash$

$\backslash$hline H & $43$ & $30$ & $1\backslash \backslash$

$\backslash$hline I & $24$ & $33$ & $10\backslash \backslash$

$\backslash$hline J & $6$ & $8$ & $3\backslash \backslash$

$\backslash$hline K & $9$ & $35$ & $14\backslash \backslash$

$\backslash$hline L & $22$ & $26$ & $3\backslash \backslash$

$\backslash$hline M & $3$ & $32$ & $10\backslash \backslash$

$\backslash$hline N & $48$ & $9$ & $3\backslash \backslash$

$\backslash$hline O & $27$ & $2$ & $7\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

The starting districts are as follows: District $1$ is made up of Customers A through $\backslash ($ F $\backslash )$ and District $2$ is made up of Customers G through O$.$