Planners for a company that makes several models of garden tractors are about to prepare an aggregate production plan that will cover the next six months. They have assembled the following information: Month ForecastdemandP12,00023,00034,00045,00052,000618,000Total Permanent workforce =140 Production per month =2,800 units or 20 per worker Initial inventory =1,000 units Desired ending inventory at the end of 6th month =1,000 units Costs Output Regular time permanent =$100 per tractor Overtime =$150 per tractor Temporary =$100 per tractor Hire cost =$500 per temporary worker or $25(=$500/20 units) per unit (charged to the first month of employment) Inventory =$10 per tractor per month (charged on the average inventory level) Backorder =$150 per tractor per month They now want to evaluate a plan that calls for level output/workforce (with the current level of permanent workforce, 140), using inventory to absorb the uneven demand but allowing some backorder. They start with 1,000 units inventory on hand in the first month and wish to end with the same amount. It is the policy of the company that the maximum amount of overtime output per month be 400 units. Suppose that the new union contract limits the number of temporary workers working in any month to 28 (i.e., 20 percent of number of permanent workers). Hint: Assume that it is possible to have different levels of Temp production across months. Using trade-off analysis and trial-and-error, find the minimum cost plan in this case. (Hint. Hire 10 temps for 3 months and 15 temps for 2 months starting in Month 3.). (Do not leave any empty spaces; input a "0" wherever it is required. Negative answers should be indicated by a minus sign.)