Manager T. C. Downs of Plum Engines, a producer of lawn mowers and leaf blowers, must develop an aggregate plan given the forecast for engine demand shown in the table. The department has a normal capacity of 130 engines per month. Normal output has a cost of $60 per engine. The beginning inventory is zero engines. Inventory carrying cost is $2 per engine per month. Backlog cost is $90 per engine per month.

1. Develop a chase plan that matches the forecast and compute the total cost of your plan using trial and error method.
2. Develop the optimal aggregate plan that matches the forecast and compute the total cost of your plan using the mathematical method (Excel Solve).
3. Please compare between the two aggregate plans, describe findings and validate the differences.