Consider the transportation problem and its initial solution in the table below.What is the improvement index for the empty cell Source 1 - Destination 3?
A)0
B)-14
C)-23
D)-70
E)115

Question

Consider the transportation problem and its initial solution in the table below.What is the improvement index for the empty cell Source 1 - Destination 3? 
A)0 
B)-14 
C)-23 
D)-70 
E)115

Quizplus · Accepted Answer

The improvement index is calculated by subtracting the lowest cost in the row or column from the second lowest cost in the same row or column.

For the empty cell in Source 1 - Destination 3:
- Row: 5, 7, -> Improvement index = 7-5 = 2
- Column: 3, 5, 7 -> Improvement index = 5-3 = 2

Since the row and column improvement indexes are equal, we can choose either the row or column with the lower cost to fill the empty cell.

The column has a lower cost (3 < 5), so we can allocate 3 units from Source 1 to Destination 3, reducing the supply at Source 1 to 4 and satisfying the demand at Destination 3.

Updated solution:
```
    | D1 | D2 | D3 | D4 | Supply
----+----+----+----+----+-------
S1  | 6  | 9  | 3  |    | 4      
----+----+----+----+----+-------
S2  |    | 5  | 7  | 8  | 7      
----+----+----+----+----+-------
S3  | 8  | 6  | 12 | 6  | 9      
----+----+----+----+----+-------
Demand | 5  | 9  | 12 | 8  |       
```

Consider the Transportation Problem and Its Initial Solution in the Table