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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.
Formulate and solve a transportation model for this problem.
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