Aggregate production in the next four quarters is set to be $300$ units in each quarter. Demand is $250,250,450,$ and $250$ units respectively in each of the next four quarters. Beginning inventory is zero. If we are unable to meet the demand, it is not lost but backordered. Cost of holding one unit in inventory per quarter is $ $2,$ and the cost of having one unit of inventory backordered per quarter is $ $8.$ In the given production plan, what is the total cost of inventory $($holding cost and backorder cost combined$)?($For simplicity, assume that all shipments take place at the end of each quarter, not during the quarter$)$