$(10$ Marks$)$ Consider the transportation table below.

$($a$)$ Find the initial solution by using northwest corner method.

$($b$)$ What is the total cost of the shipping plan that is obtained by performing two iterations of stepping stone method? Show all of your work

From$/$To $($A$)($B$)($C$)$ Supply

$($W$)54350$

$($Y$)42640$

$($Z$)37940$

Demand $403060$