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Which one of the following conditions should be satisfied for the application of optimality test on an initial solution of transportation model?
  • a)
    Number of allocations should be less than m + n − 1
  • b)
    Number of allocations should be equal to m + n − 1
  • c)
    Number of allocations should be equal to m + n
  • d)
    Number of allocations should be more than m + n
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Which one of the following conditions should be satisfied for the app...
Optimality Test for Transportation Model
Transportation models are used to minimize transportation costs while satisfying supply and demand constraints. In order to apply the optimality test to an initial solution of a transportation model, the following condition should be satisfied:

Number of Allocations = m + n - 1

Explanation:

1. Number of Allocations
- The number of allocations refers to the number of cells in the transportation table that are filled with values representing the amount of goods transported from sources to destinations.
- Each allocation represents a decision on how much to transport from a source to a destination.

2. Formula for Number of Allocations
- The formula for the number of allocations in a transportation model is m + n - 1, where m is the number of sources and n is the number of destinations.
- This formula accounts for the fact that each row (source) and each column (destination) should have at least one allocation, and the total number of allocations should not exceed this limit.

3. Application of Optimality Test
- In order to apply the optimality test to an initial solution, the number of allocations should be exactly equal to m + n - 1.
- This condition ensures that the initial solution is feasible and balanced, allowing for the evaluation of optimality based on the allocation of goods between sources and destinations.
Therefore, the correct condition for the application of the optimality test on an initial solution of a transportation model is that the number of allocations should be equal to m + n - 1.
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Which one of the following conditions should be satisfied for the application of optimality test on an initial solution of transportation model?a) Number of allocations should be less than m + n − 1b) Number of allocations should be equal to m + n − 1c) Number of allocations should be equal to m + nd) Number of allocations should be more than m + nCorrect answer is option 'B'. Can you explain this answer?
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