The current aggregate demand requirements for a firm are shown below for the next six months:$($May $120,$ June $100,$ July $100,$ Aug $100,$ Sept $130,$ Oct $150)$The firm always plans to meet all demand. The firm currently has $120$ workers capable of producing $120$ units in a month $(1$ unit$/$worker$).$ The workforce can be increased $($at a cost of $$500$ per worker$)$ or decreased $($at a cost of $$1,000$ per worker$).$ Inventory holding cost is $$100$ per unit per month. The firm currently has $40$ units of inventory on hand, and it would like to have $40$ units available at the end of each month. Regular production cost is $$3,000$ per unit.a$.$ What should the aggregate plan be if the inventory holding cost is to be minimized?b$.$ What is the cost of this plan?