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A company has signed the following contract to supply customers A and B for the next three months.
June July August
Customer A 30 20 15
Customer B 20 20 10
They can produce 40 units per month at a cost of $100 per unit on regular time and an additional 10 units per month on overtime at a cost of $120 per unit. They can store units at a cost of $ 10 per unit per month. The contract allows the company to fall short on its supply commitment to customer A during the month of June and July, but this incurs a penalty cost of $ 5 per unit, however, all shipments are to be completed by August. No shortages are allowed for customers B and his demand must be satisfied on the months specified.
The company wishes to determine the optimal production schedule that will minimize the total cost of production, storage and shortage.
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