Consider the transportation problem and its optimal solution in the tables below.The cell Source 3 - Destination 3 is currently empty.What would be the change in the total shipping cost if the largest possible amount were shipped using that route,leaving all the supply and demand conditions unchanged?
A)0
B)fifty units
C)a decrease of $9
D)an increase of $450
E)an increase of $630

Question

Consider the transportation problem and its optimal solution in the tables below.The cell Source 3 - Destination 3 is currently empty.What would be the change in the total shipping cost if the largest possible amount were shipped using that route,leaving all the supply and demand conditions unchanged? 
A)0 
B)fifty units 
C)a decrease of $9 
D)an increase of $450 
E)an increase of $630

Quizplus · Accepted Answer

The largest possible amount that can be shipped using Source 3 - Destination 3 is the smaller of the supply and demand values, which is 150. If we ship 150 units using this route, the new transportation table will be:

|    | Dest 1 | Dest 2 | Dest 3 | Supply |
|----|--------|--------|--------|--------|
| S1 | 50     | 0      | 0      | 50     |
| S2 | 0      | 100    | 0      | 100    |
| S3 | 0      | 50     | 150    | 200    |
| Demand | 50 | 150 | 150 |        |

The total shipping cost would increase by $450, because the cost of shipping 150 units from Source 3 to Destination 3 is $3 per unit, making the total additional cost $450 (150 units x $3).

Consider the Transportation Problem and Its Optimal Solution in the Tables