Q$2)$ Suppose the U$.$S$.$ pharmaceutical company has $3$ factories supplying the warehouses for $3$ major consumers and its management wants to determine the minimum$-$cost shipping schedule for its monthly output to these customers. Factory supply, warehouse demand, and shipping costs per case for these drugs are shown in following table.

Data for U$.$S$.$ pharmaceutical transportation problem

$\backslash$table$[[$Factory$,$Supply,warehouse,demand$],[$Indianapolis$,50,$Columbus,$40],[$Phoenix$,30,$St$.$ Louis,$60],[$New York,$75,$Denver,$55]]$

Shipping costs per case $($in dollars$)$

$\backslash$table$[[$From To$,$Columbus,St$.$ Louis,Denver$],[$Indianapolis$,30,30,5],[$Phoenix$,10,10,10],[$New York,$20,10,35]]$

Please indicate the optimum low$-$cost transportation plan for the U$.$S$.$ pharmaceutical company

$($i$)$ By using northwest corner method and then stepping stone approach. Show details of your calculation, show all the possibilities, and calculate total cost for each step.

$($ii$)$ By using excel solver