Problem $5$ Mincost flow problem $(15$ points$)$

Reduce the following optimization problem as a minimum cost flow problem, i$.$e$.,$ draw the graph and specify the flow conservation and flow bound constraints. $($Hint: Consider manipulating the inequations$/$equations$).$

$minimiz{e}_x,c^{T}x$

subject $to{x}_2+x_4+x_{5}5$

$,x_1+x_2+x_{5}12$

$,x_1+x_2+x_{3}10$

$,x_1+x_2+x_{3}6$

show this by drawing graph