Discuss the below:
Q: 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.
|
|
|
Customer
|
|
I
|
2
|
|
4
|
|
Plant
|
1
|
$ROO
|
$700
|
$500
|
$200
|
|
2
3
|
$500
$600
|
$200
|
$100
|
$300
|
|
$400
|
$300
|
$500
|
a) Formulate this problem as a transportation problem where the objective function is to be maximized by constructing the appropriate balanced transportation (parameter) tableau that gives unit profits.
b) Write the LP model for this problem.