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 135 engines per month. Regular output has a cost of $62 per engine. The beginning inventory is zero engines. Overtime has a cost of $112 per engine. Month 1 2 3 4 5 6 2 8 Total Forecast 126 135 148 128 125 125 132 155 1332 a. Develop a chase plan t'iat 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.) Period 1 2 I 3 4 5 I 6 Ti" 3 Total Forecast 120 135 I 140 120 125 I 125 132 135 I 1.032 Output -E Costs Output H EEEEEEEEE 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 $135 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.) Forecast | 120|| 135|| 14o|| 120|| 125|| 125|| 132|| 135\" 1.032 Output lnve ntory Beginning Ending Average Backlog Costs Output iii EEEEEEEEE