$(2)$ Find an optimal solution for the following transportation problem.

TO

FROM

Valley

$($V$)$

Town

$($T$)$

Junction

$($J$)$

Burg

$($B$)$ Supply

Macon

$($M$)$

$$6$ $$8$ $$7$ $$4$

$30050350$

York

$($Y$)$

$$3$ $$10$ $$2$ $$9$

$150250200600$

Perry

$($P$)$

$$14$ $$4$ $$9$ $$12$

$250250$

Demand $3002002504501,200$

The above feasible plan is obtained by applying the Northwest Corner Rule $($e$.$g$.,300$ fro