Given the following Transportation Problem:

$\backslash$table$[[$FROM$,$TO$,$A$.$ ALBUQUERQUE,$\backslash$table$[[$B$.],[$BOSTON$]],\backslash$table$[[$C$.],[$CLEVELAND$]],$FACTORY CAPACITY$],[$D$.$ DES MOINES,$5,4,3,100],[$E$.$ EVANSVILLE,$8,4,3,300],[\backslash$table$[[$F$.$ FORT$],[$LAUDERDALE$]],9,7,5,300],[$WAREHOUSE DEMAND,$300,200,200,700]]$

a$.$ Use the North$-$West Corner Rule to find the initial solution

b$.$ Find the optimal solution