The demand for a perishable item over the next four months is $400,300,420,$ and $380$ tons,

respectively. The supply capacities for the same months are $500,600,200,$ and $300$ tons. The purchase

price per ton varies from month to month and is estimated at $$100,$ $$140,$ $$120,$ and $$150,$ respectively.

Because the item is perishable, a current month$$s supply must be consumed within $3$ months $($starting

with current month$).$ The storage cost per ton per month is $3$$$.$ The nature of the item does not allow

back$-$ordering. Formulate the problem as a transportation model and find an initial solution by

Northwest$-$corner method.