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 145 engines per month. Regular output has a cost of $60 per engine. The beginning inventory is zero engines. Overtime has a cost of $110 per engine. Month Forecast 1 128 2 135 3 143 4 5 165 125 6 125 7 140 8 143 Total 1,104 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 "O" wherever required.) Period 2 3 4 5 Forecast 128 135 143 165 125 125 140 143 7 8 Total 1,104 Output Regular 128 135 143 145 125 125 140 143 Overtime 0 20- 0 0 0 1,084 20 Output - Forecast 0 0 0 0 0 Costs Output Regular Overtime $7,680 8,100 8,580 8,700 7,500 7,500 8,400 8,580 0 0 2,200 0 0 0 0 65,040 2,200 $ $7,680 8,100 8,580 10,900 7,500 7,500 8,400 8,580 Total 67,240 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 $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 "O" wherever required. Round average Inventory row, Inventory cost row, and Total row values to 1 decimal.) Period Forecast 2 3 5 6 8 Total 128 135 143 165 125 125 140 143 1,104 Output Regular 138 138 138 138 138 138 138 138 1,104 Output - Forecast 10 3 -5 -27 13 13 -2 -5 Inventory Beginning 0 10 13 8 (19) X (6) X 7 5 Ending 10 13 8 (19) X Average 5.0 11.50 10.5 Backlog (10) (13) (8) (5.5)x 19 (6) (12.5)x 6 7 5 0 0.5 x (7) 6.0 (5) 2.50 Costs Output Regular Inventory Backorder Total $ 8,280 8,280 10.0 0 23.0 8,280 21.0 8,280 8,280 8,280 8,280 8,280 66,240 0 0 0.0 x 2,375 0.0 750 1.0 0 12.0 0 5.0 72 x 0 3,125 $ 8,303.0 8,301.0 10,655.0 9,030.0 8,281.0 8,292.0 8,285.0 8,290.0 69,437