# Question: The Onenote Co produces a single product at three plants

The Onenote Co. produces a single product at three plants for four customers. The three plants will produce 60, 80, and 40 units, respectively, during the next time period. The firm has made a commitment to sell 40 units to customer 1, 60 units to customer 2, and at least 20 units to customer 3. Both customers 3 and 4 also want to buy as many of the remaining units as possible. The net profit associated with shipping a unit from plant i for sale to customer j is given by the following table:

Management wishes to know how many units to sell to customers 3 and 4 and how many units to ship from each of the plants to each of the customers to maximize profit.

(a) Formulate this problem as a transportation problem where the objective function is to be maximized by constructing the appropriate parameter table that gives unit profits.

(b) Now formulate this transportation problem with the usual objective of minimizing total cost by converting the parameter table from part (a) into one that gives unit costs instead of unit profits.

(c) Display the formulation in part (a) on an Excel spreadsheet.

Management wishes to know how many units to sell to customers 3 and 4 and how many units to ship from each of the plants to each of the customers to maximize profit.

(a) Formulate this problem as a transportation problem where the objective function is to be maximized by constructing the appropriate parameter table that gives unit profits.

(b) Now formulate this transportation problem with the usual objective of minimizing total cost by converting the parameter table from part (a) into one that gives unit costs instead of unit profits.

(c) Display the formulation in part (a) on an Excel spreadsheet.

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