8.1-6. The One note 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.