The planner for a company that makes garden tractors is about to prepare an aggregate production plan that will cover the next six months. She has collected the following information: Permanent workforce =140 Production per month =20 per worker Initial inventory =1000 units Costs Regular time permanent workforce =$100 per tractor Overtime =$150 Temporary =$100 per tractor Hire cost =$500 per temporary worker or $25(=$500/20 units) per unit charged to the first month of employment; assume that temporary workers have the same productivity as permanent workers Holding =$10 per tractor per month (charged on the average inventory level) Back order =$150 per tractor per month Question 1. The planner wants to evaluate a production plan that calls for level output/workforce (with the current level of permanent workforce, 140) using inventory to absorb the uneven forecast demand but allowing some back order. Question 2. The planner has decided to investigate the use of overtime to make up the shortage , It is the policy of the company that the maximum amount of overtime output per month be at most 350 units. Develop an aggreage production plan in this case and compare it to plan 1. Question 3. The third option is to use temporary workers. Suppose that temporary workers will be working during a second shift and enough of them are available. Develop an aggregate production plan in this case. It is noteworthy that overtime is not possible in this case. Bonus Question. Assume that the manager is allowed to have overtime workers in addition to the temporary and permanent workers. Please develop an aggreagte operations plan using MS. EXCEL Solver which minimizes the totla cost over the planning horizon? Aggregate Planning Relationships 1. To determine ending inventory and back order in any period i, first calculate X : X=Beginninginventoryi+(OutputForecastIBackorderi where output = sum of regular, overtime, and part-time production. If X0, then ending inventory i=X and backorderi=0; If X