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 (in truckloads):

The regular production can be supplemented by up to 30 truckloads a month from overtime. Determine the production plan that has the lowest total cost.

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Month May Jun Jul Aug Sept Oct Total Forecast 50 60 70 90 80 70 420 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 Back-order cost $5,000 per truckload per month Beginning inventory