Cooltoys demand for their product mix for the upcoming year is given as follows:

Month	Demand
January	2700
February	2520
March	2880
April	3340
May	2980
June	2780
July	3600
August	2980
September	3960
October	3960
November	3220
December	1920

The company has a starting inventory in January of 1,500 toys. At the beginning of January, the company has a workforce of 60 employees. The plant has a total of 20 working days in each month, and each employee works eight hours per day on straight time and the rest on overtime. The capacity of the production operation is determined primarily by the total labor hours worked. Because of labor rules, no employee works more than 10 hours of overtime per month. Aggregate costs are:

Item	Cost
Material cost	$13/unit
Inventory holding cost	$2/unit/month
Marginal cost of stockout/backlog	$5/unit/month
Hiring and training costs	$400/worker
Layoff cost	$700/worker
Labor hours required	4/unit
Regular time cost	$6/hour
Overtime cost	$9/hour
Cost of subcontracting	$60/unit

• There are no limits on subcontracting, inventories, and stockouts/backlog.
• All stockouts are backlogged and supplied from the following months production.
• Inventory costs are incurred on the ending inventory in the month.
• The supply chain managers goal is to obtain the optimal aggregate plan that allows the manufacturer to end December with at least 500units meeting all demand.

1. Assuming no backlogs, no subcontracting, and no new hires, what is the optimum production schedule? What is the annual cost of this schedule? What is the profit when selling price is $100?
2. How would the optimal aggregate plan change if hiring-training cost was $40, and layoff cost was $70? What is the new total cost and profit?