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 1 2 3 4 5 6 7 Total 1,184 Forecast 128 135 143 165 125 125 140 143 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.) Period 2 3 4 5 6 7 8 Forecast 128 135 143 165 125 125 140 Output 128 135 ? 143 145 125? 125?? 140 0? 0? 0? 0? 0? 0? Regular Overtime Output - Forecast Costs Output Regular Overtime Regular Output - Forecast Inventory Beginning Ending Average 0? 0 0 $7,680 8,100 8,580 8,700 7,500 7,500 8,400 8,580 0 0 2,200 0 Total $7,680 8,100 8,580 10,900 7,500 7,500 8,400 8,580 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 "0" wherever required. Round average Inventory row, Inventory cost row, and Total row values to 1 decimal.) Period 2 3 4 5 7 8 Forecast 128 135 143 165 125 125 140 143 Output 138? 138 138 138 138 138?? 138 138 10 ? -5 -27? 13 13? -2 -5 0? 13? (19) X (6) X 8? (19) X 10 ? 8? (6) X 7? 5.0? (5.5) X 0.5 X (12.5) X 6 (10) X (8) X 19? (7) X 8,280 8,280? 0.0 750 1.0 X 0? 9,030.0 8.281.0 X Backlog Costs Output Regular Inventory Backorder Total $ 8,280 10.0? 0? $ 8,290.0 3? 10? 13? 11.50 (13) 8,280 23.0 0? 0? 0? 8,303.0 0? 10.5 8,280 21.0 20? 0? 0 8,301.0 8,280 0.0 x 2,375? 10,655.0 X 0? ? 0? 7? 5? 6.0? (5) 8,280 12.0 0? 143 143 8,292.0 0? 0? 0? 5? 0? 2.50 0 8,280 5.0 0 8,285.0 Total 1,104 1,084 20 65,040 2,200 67,240 S $ Total 1,104 1,104 S 66,240 72 X 3,125 S 69,437