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 amounts should be indicated by a minus sign. Leave no cells blank - be certain to enter " 0 " wherever required.) Compare the costs to a level plan that uses inventory to absorb fluctuations. Inventory carrying cost is $2 per engine per month. acklog cost is $90 per engine per month. There should not be a backlog in the last month. Atsume that using overtime is not an ption. (Negative amounts should be indicated by a minus sign. Leave no cells blank - be certain to enter " 0 " wherever required. 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. (Negative amounts should be indicated by a minus sign. Leave no cells blank - be certain to enter " 0 " wherever required.)