Problem $1.(10$ points$)$

Draw the network representation of the following network flow problem. Your network should be

represented with nodes and links $($or connections$)$ between them. Also add values $($in numbers$)$ to every

node and every link.

MIN: $7x_{12}+6x_{14}+3x_{23}+4x_{24}+5x_{32}+9x_{43}+8x_{52}+5x_{54}$

Subject $to$: $-x_{12}-x_{14}=-5$

$,+x_{12}+x_{52}+x_{32}-x_{23}-x_{24}=+4$

$,-x_{32}+x_{23}+x_{43}=+8$

$,+x_{14}+x_{24}+x_{54}-x_{43}=+0$

$,-x_{52}-x_{54}=-7$

$,x_{ij}0$ for all i and $j$