Trexoid Inc. makes a popular video game console. Demand varies each month, with highest demand coming in the last quarter of the year. Regular production costs are $$120$ per unit and inventory carrying cost is $$5$ per unit per quarter. Overtime production cost is $$150$ per unit. Assume that the $10$ current Trexoid employees can produce a total of $50,000$ units per quarter in regular production and can work enough overtime hours to produce the amount required if a chase plan is employed. On the other hand, hiring cost is $$5,000$ per employee and firing cost is $$10,000$ per employee. Trexoid currently has zero inventory on hand, and they would like to have zero inventories at the end of the year. Assume hiring and layoff$/$firing$,$ if necessary, occur at the beginning of the quarter. Forecast demand is as follows:

Quarter $130,000$ units

Quarter $220,000$ units

Quarter $370,000$ units

Quarter $4120,000$ units