Question TWO: $(7\mathrm{.}5$ Marks$)$

Inventory manager for a company that makes several models of low$-$cost cars is about to prepare the aggregate plan that will cover six months. The plan calls for a steady rate of regular output, mainly using inventory to absorb the uneven demand but allowing some backlog. They intend to start with $40$ units as inventory on hand in the first month. The planned ending inventory is zero. The expected demand forecast is as follows:

$\backslash$table$[[$Month$,1,2,3,4,5,6],[$Forecast$,50,80,100,90,50,30]]$

Cost:

Regular time $=$$$600$ per car

Overtime $=$$$800$ per car

Subcontract $=$$$900$ per car

Inventory $=$$$200$ per car per period on average inventory

Back orders $=$$$500$ per car per period

Required:

If overtime and subcontract are NOT allowed. Prepare the aggregate plan and calculate its cost. $($Fill the following plan$).$

$6$