Problem $1$: Obtain initial feasible solution for the following Transportation problem shown in the table below using the following methods:

North West Corner Rule $($NWCR$)$

North East Corner Rule $($NECR$)$

Least Cost Method

Vogle's Approximation Method $($VAM$)$

$\backslash$table$[[Sid{j}^{dj},$A$,$B$,$C$,$D$,$Supply$],[E,,30,,8,,8,,11,30],[F,,5,,11,,9,,20,40],[$G$,,8,,9,,7,,18,50],[$Demand$,35,,28,,32,,25,,]]$