$.$ Consuelo chua, inc, is a disk drive manufacturer in need of an aggregate plan for July through becember. The company has gathered the following data:

cost

Holding cost $$8/$disk$/$month

Subcontracting $$80/$disk

Regular$-$time labor $$12/$hour

Overtime labor $$18,$ hour for hours above $8$hours worker$/$day

Hiring cost $$40/$worker

Layoff cost $$80/$worker

demand

July $400$

Aug $500$

Sept $550$

Oct $700$

Nov $800$

dec $700$

No costs are inoccured for unmet demand but unmet demand backorders must be handeled in the following period. If half or more of a worker is needed roundup