Question $1(25$ marks$)$:

We want to assign exactly each of the nodes in the left$-$hand$-$side nodes to exactly one of the right$-$hand$-$side nodes $($one to one assignment$).$ Use the Hungarian method to obtain the minimum cost assignment.

Show each step clearly $(15$ pts$)$ and report an optimal solution $(5$ pts$)$ and its objective value $(5$ pts$).$

The numbers on the arcs show the assignment costs. $($e$.$g$.$ assigning node $1$ to node B costs $7)$

If there is no arc between two nodes, then assignment is not allowed between them. $($e$.$g$.$ assigning node $1$ to node C is not allowed$)$

$5$

$1$

$7$

A

$8$

$2$

$6$

B

$3$

$4$

$5$

$3$

$2$