A transportation problem involves the following costs, supply, and demand:

$\backslash$table$[[,$To$,],[$From$,1,2,3,4,$Supply$],[1,$$$500,$$$750,$$$300,$$$450,12],[2,650,800,400,600,17],[3,400,700,500,550,11],[$Demand$,10,10,10,10,]]$

a$.$ Find the initial solution using the northwest corner method, the minimum cell cost method, and Vogel's approximation model. Compute total cost for each.

b$.$ Using the VAM initial solution, find the optimal solution using the modified distribution method $($MODI$).$