Question $4$:

$4.$ A manager has prepared a forecast of expected aggregate demand for the next six months. Develop an aggregate production plan to meet this demand given this additional information: A level production rate of $100$ units per month will be used. Backorders are allowed, and they are charged at the rate of $$8$ per unit per month. Inventory holding costs are $$1$ per unit per month. Determine the cost of this plan if regular time cost is $$20$ per unit and beginning inventory is zero.

$\backslash$table$[[$Month$,$Forecast$],[1,100],[2,80],[3,120],[4,120],[5,100],[6,80]]$