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 136 engines per month. Regular output has a cost of $50 per engine. The beginning inventory is zero engines. Overtime has a cost of $110 per engine. 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.) b. Compare the costs to a level plan that uses inventory to absorb fluctuations. Inventory carrying cost is $3 per engine per month. Backlog cost is $125 per engine per month. There should not be a backlog in the last month. Set regular production equal to the monthly average of total forecasted demand. 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. Round average inventory row, Inventory cost row, and Total row values to 1 decimal.)