A spring$-$water bottling company has recently expanded into flavoured water. The marketing manager is predicting an upturn in demand based on the new offerings and the increased public awareness of the health benefits of drinking more water. She has prepared aggregate forecasts for the next six months, as shown below $($in truckloads$)$: Month May Jun Jul Aug Sept Oct Total Forecast $506070908070420$ The production manager has gathered the following information: Regular production cost $$1,000$ per truckload Regular production capacity $60$ truckloads per month using $20$ employees Overtime production cost $$1,500$ per truckload Holding cost $$200$ per truckload per month Backorder cost $$5,000$ per truckload per month Beginning inventory $0$ The regular production can be supplemented by up to $30$ truckloads a month from overtime. Determine the plan that has the lowest total cost. Hint: Use overtime in August$$October$.($Do not leave any empty spaces; input a $"0"$ wherever it is required. Negative answers should be indicated by a minus sign.$)$ Period May Jun Jul Aug Sep Oct Total Forecast $506070908070420$ Output Regular Overtime Output $-$ Forecast Inventory Beginning Ending Average Backorder Costs: Regular @ $$1,000$ Overtime @ $$1,500$ Inventory @ $$200$ Backorder @ $$5,000$ Total $