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National Steel Corporation (NSC) produces special-purpose steel used in the aircraft and aerospace industries. The sales department has received orders for the next four months. January February March April Demand (tons) 2300 2000 3100 3000 NSC can meet demand by producing the steel, by drawing from its inventory, or a combination of these. No backlogs are allowed. Inventory at the beginning of January is 300 tons. Production costs are expected to rise in February and March. Production and inventory costs are: January February March April Production cost 3000 3300 3600 3600 Inventory cost 255 255 255 255 Product costs are in $ per ton. Inventory costs are in $ per ton per month. NSC can produce at most 3000 tons of steel per month. The production level in December was 2600 tons. However, changes in production levels from month to month result in additional costs. For example, NSC would have to incur significant costs in hiring and training workers to increase production to 3000 tons in January. Similarly, NSC could not cut production from 2600 tons to 2000 tons without incurring substantial costs for worker layoff, mothballing systems, etc. Management estimates that it costs $110 per ton increase in production and $90 per ton decrease in production. Formulate and solve an LP model to determine the production plan that meets demand at the minimum cost taking into account these “hiring and firing” costs. Please define your decision variables, objective function and constraints and label your constraints clearly and label your constraints clearly. You need to show your work in problem formulation, and its implementation in Excel, and the answer report generated by Excel Solver.
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