The current aggregate demand requirements for a firm are shown below for the next six months

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 $1000 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 at least 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?

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Month My July Aug Sept Oct Demand 120 100 100 100 130 150