$*5.$ 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. Solve the problem as a transportation model and determine the optimum delivery schedule for the item over the next $4$ months.