The following linear programming formulation is for a transshipment problem.

Min $11$x$13+12$x$14+10$x$21+8$x$34+10$x$35+11$x$42+9$x$45+12$x$52$

s$.$t$.$

x$13+$ x$14$ x$21<=5$

x$21$ x$42$ x$52<=3$

x$13$ x$34$ x$35<=6$

$$ x$14$ x$34+$ x$42+$ x$45<=2$

x$35+$ x$45$ x$52<=4$