You do not need to get solution. Please indicate and explain all relevant information/assumptions explicitly.An international company aims to make the production, inventory and workforce plans for one of its production facilities. They obtained the following demand data for their system in a unit of tons during last 6 months. Month Demand Forecast Production Days 1 260 20 2 290 25 3 420 20 4 230 15 5 250 19 6 230 15 In their planning process, they will use three ahead moving average method (N=2) to predict the future demand data for next 6 months. There are currently 100 workers employed at the company. It is observed that, over a period of 30 working days, 20 workers produced 120 tons. The cost of hiring up to 25 workers is $750, and after 25 hires cost decreases to $600. Firing a worker costs $550. Inventory holding cost is $40 per ton per month. At the beginning of the planning period, the company has no materials in the stock. The company wants to have at least 100 ton in inventory at the end of 2nd month and plans to start 6th month with 150 tons in the stock. Some of the demand can also be allowed not to be satisfied for next 6 months. If company can not satisfy its customers, cost of this situation will be $45 per ton. a) Please write down an open - f orm mathematical model to get optimal solution for this problem.