Consider a problem of scheduling the weekly production of a certain item for the next 4 weeks. The production cost of the item is $ 10 for the first two weeks, and $ 15 for the last two weeks. The weekly demands are 300, 700, 900, and 800, which must be met. The plan can produce a maximum of 700 units each week. In addition the company can employ overtime during the second and third week. This increases the weekly production by an additional 200 units, but the production cost increases by $ 5 per item. Excess production can be stored at a unit cost of $ 3 per week. How should the production be scheduled to minimize the cost of production? Formulate the problem as transportation model without backorder and solve it.
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