Cooltoys sells each product mix through a retailer called Allkids for $55. All toys are produced and stored in Allkids warehouses. Assume everything else is the same as Question 1 without the changes in hiring/firing costs. Therefore, Allkids have a beginning inventory of 1500 toys and they aim to finish the year with an inventory of 500 units.

Allkids estimates that discounting a Cooltoys toy from $55 to $54 (a $1 discount) in any period results in the period demand increasing by 30 percent because of increased consumption or substitution. Further, 10 percent of each of the three following months demand is moved forward. Management would like to determine whether it is more effective to offer the discount in January or July.

a. What is the optimal aggregate plan and how is the total profit effected if the promotion offered in January?

b. What is the optimal aggregate plan and how is the total profit effected if the promotion offered in July?

c. Compare the two options by considering the impact of a promotion on demand and the resulting optimal aggregate plan.

Please show detailed work, with formulas used.

Q1

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

   Month	Demand
   January	2600
   February	2000
   March	2900
   April	1400
   May	2100
   June	2400
   July	3400
   August	3300
   September	2100
   October	1900
   November	2600
   December	1700

The company has a starting inventory in January of 1,500 toys. At the beginning of January, the company has a workforce of 50 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	$12/unit
Inventory holding cost	$3/unit/month
Marginal cost of stockout/backlog	$5/unit/month
Hiring and training costs	$400/worker
Layoff cost	$600/worker
Labor hours required	4/unit
Regular time cost	$6/hour
Overtime cost	$9/hour
Cost of subcontracting	$45/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 500 units 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?
2. How would the optimal aggregate plan change if hiring-training cost was $40, and layoff cost was $60? What is the new total cost and profit?