$\backslash$table$[[\backslash$table$[[$Distribution$],[$Centers$]],$Pennsylvania $$30,,$Charlotte,Philadelphia,Chicago,Boston,Capacity$],[$$$10,$$$24,$$$24,$$$25,$$$21,21,000],[$Virginia$,$$$16,$$$13,$$$30,$$$22,$$$10,$$$24,28,000],[$North Carolina,$$25,$$$22,$$$21,$$$10,$$$20,$$$11,19,000],[\backslash$table$[[$South$],[$Carolina$]],$$$19,$$$23,,$$$22,$$$13,$$$26,24,000],[$Georgia$,$$$19,$$$12,$$$17,$$$23,$$$11,$$$22,28,000],[$Ohio$,$$$21,$$$26,$$$28,$$$17,$$$13,$$$26,25,000],[$Demand$,25,400,32,000,24,500,25,000,18,50,19,50,]]$

a$)$ Find the fesible solution using the north west strategy

The number of shipments made from Pennsylvania to NY is $21,000.$

The number of shipments made from South Carolina to Philadelphia is $14,000.$

The total cost of the feasible plan is $2,425,500.$

b$)$ Using the solver in Excel with the optimal cost, the optimal plan is $125,500$ cheaper than the feasible plan obtained using the north west strategy above.