The initial cost of a transportation problem using NWC Method is Rs. 45000 and by VAM Method it is Rs. 39500. The optimal Cost would be: Select one: a. Less than or equal to Rs. 39500 b. Rs. 39500 c. Rs. 45000 d. Between Rs. 39000 & Rs. 45000
Answers
Answer: The optimal cost would be Rs. 39500, which is the initial cost obtained using Vogel's Approximation Method (VAM).
The transportation problem is a mathematical model used to determine the optimal allocation of resources from various sources to different destinations. The objective is to minimize transportation costs. There are several methods to solve the transportation problem, and Vogel's Approximation Method (VAM) is one of them.
Here is a step-by-step explanation of how to solve a transportation problem using the VAM method:
Determine the supply and demand: The first step is to determine the supply and demand at each source and destination, respectively. The total supply should equal the total demand.
Create a transportation table: A transportation table should be created with the supply and demand data. The table will have the sources on one axis and the destinations on the other axis.
Calculate the opportunity cost: The opportunity cost is the difference between the lowest supply and the highest demand for each row and column of the transportation table. These values will be used to determine which cell to fill in next.
Select the cell with the maximum opportunity cost: The cell with the highest opportunity cost should be selected and filled in with the maximum possible allocation that can be made from the available supply.
Update the opportunity cost: The opportunity cost should be updated after each allocation is made. The supply and demand values for the corresponding row and column should be updated to reflect the changes made in the previous step.
Repeat the process until all cells have been filled in: Continue repeating the process of selecting the cell with the maximum opportunity cost and updating the opportunity cost until all cells have been filled in.
Calculate the total cost: The total cost of transportation can be calculated by summing up the transportation cost for each cell in the transportation table.
By following these steps, you can solve a transportation problem using the VAM method and determine the optimal transportation cost. In the example provided, the initial cost obtained using the VAM method is Rs. 39500, which is the optimal cost.
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Answer:
The correct answer to the question is option (a) "Less than or equal to Rs. 39500".
Step-by-step explanation:
The transportation problem refers to the problem of distributing goods from several sources to several destinations. There are various methods to solve a transportation problem, such as the Northwest Corner (NWC) method and the Vogel's Approximation Method (VAM). The initial cost of the transportation problem using NWC method is Rs. 45000, while by VAM method it is Rs. 39500.
To find the optimal cost, we need to solve the transportation problem using any of the methods and obtain the minimum cost. The optimal cost is the minimum cost required to transport the goods from the sources to the destinations.
Since the initial cost obtained by the VAM method is lower than that obtained by the NWC method, it is more likely that the optimal cost would also be less than or equal to Rs. 39500. However, it is not possible to determine the exact optimal cost without actually solving the transportation problem.
Therefore, the correct answer to the question is option (a) "Less than or equal to Rs. 39500".
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