Determine the initial feasible solution for the following transportation problem using North$-$West Corner Method, Least Cost Method and Vogel's Approximation Method. Which of these methods give the least cost?

$(10)$

$\backslash$table$[[$Warehouse$],[$Plant$,$X$,$Y$,$z$,$W$,$Supply,$],[$A$,3,2,5,2,15,],[$B$,2,1,4,4,24,],[$C$,2,3,4,3,21,],[$Demand$,13,12,16,19,60,]]$