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 regular output capacity of 130 engines per month. Regular output has a cost of $60 per engine. The beginning inventory is zero engines, Overtime has a cost of $90 per engine. Click here for the Excel Data File a. Develop a chase plan that matches the forecast and compute the total cost of your plan. Regular production can be less than regular capacity. (Negative omounts should be indicated by o minus sign. Leave no cells blank- be certain to enter " 0 wherever reauired.I b. Compare the costs to a level plan that uses inventory to absorb fluctuations, Inventory carrying cost is $2 per engine per month Backlog cost is $90 per engine per month. There should not be a backlog in the last month. Assume that using overtime is not an option. (Negotive omounts should be indicoted by o minus sign. Leove no cells blank - be certain to enter " 0 " wherever required.)