Consider the transportation problem having the following parameter table:

$\backslash$table$[[,,$Destination,Supply$],[,,A,B,C,D,],[$Source$,1,3,1,7,4,300],[2,2,6,5,9,400],[3,8,3,3,2,500],[\backslash$table$[[$Deman$],[$d$]],,250,350,400,200,]]$

Use each of the following methods to obtain an initial BF solution. Compare the values of the objective function for these solutions.

$($a$)$ Northwest corner rule. $($NCM$)$

$($b$)$ Least Cost Cell Method $($LCM$)$

$($c$)$ Vogel's approximation method $($VAM$)$

$($d$)$ Use the solution obtained in Vogel's approximation method $($VAM$)$ and check if the solution is optimal using the MoDi method$($UV method$)$