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Consider the following statements:
In a transportation problem, North-West corner method would yield
1. An optimum solution
2. An initial feasible solution
3. Vogel's app roximat e solution
1. An optimum solution
2. An initial feasible solution
3. Vogel's app roximat e solution
Of these statements:
- a)1 alone is correct
- b)2 alone is correct
- c)3 alone is correct
- d)2 and 3 are correct
Correct answer is option 'B'. Can you explain this answer?
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Consider the following statements:In a transportation problem, North-W...
Statement 2 alone is correct
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Consider the following statements:In a transportation problem, North-W...
Transportation Problem and North-West Corner Method
Transportation problem is a kind of linear programming problem that deals with the transportation of a commodity from several sources to several destinations. The objective is to minimize the total cost or maximize the total profit, subject to the supply and demand constraints.
North-West Corner Method is one of the initial solution methods for the transportation problem. It starts by allocating the maximum possible amount of the commodity from the top-left (north-west) corner of the transportation matrix, and then iteratively filling the remaining cells according to certain rules until all the supply and demand are satisfied.
Statements and Explanation
Statement 1: North-West corner method would yield an optimum solution.
This statement is incorrect. North-West corner method only provides an initial feasible solution that may or may not be optimal. It does not guarantee the optimality of the solution. Other methods such as the stepping stone method or the modified distribution method are usually used to improve the initial solution and obtain the optimal solution.
Statement 2: North-West corner method would yield an initial feasible solution.
This statement is correct. North-West corner method provides a feasible solution that satisfies the supply and demand constraints. However, it may not be the optimal solution.
Statement 3: North-West corner method would yield Vogel's approximate solution.
This statement is incorrect. Vogel's approximation method is a different initial solution method that is based on the difference between the two smallest transportation costs in each row and column of the transportation matrix. It is usually more accurate than the North-West corner method in terms of the total cost.
Conclusion
Therefore, the correct answer is option 'B' - statement 2 alone is correct. North-West corner method provides an initial feasible solution for the transportation problem, but it does not guarantee the optimality of the solution. Other methods are usually used to improve the initial solution and obtain the optimal solution.
Transportation problem is a kind of linear programming problem that deals with the transportation of a commodity from several sources to several destinations. The objective is to minimize the total cost or maximize the total profit, subject to the supply and demand constraints.
North-West Corner Method is one of the initial solution methods for the transportation problem. It starts by allocating the maximum possible amount of the commodity from the top-left (north-west) corner of the transportation matrix, and then iteratively filling the remaining cells according to certain rules until all the supply and demand are satisfied.
Statements and Explanation
Statement 1: North-West corner method would yield an optimum solution.
This statement is incorrect. North-West corner method only provides an initial feasible solution that may or may not be optimal. It does not guarantee the optimality of the solution. Other methods such as the stepping stone method or the modified distribution method are usually used to improve the initial solution and obtain the optimal solution.
Statement 2: North-West corner method would yield an initial feasible solution.
This statement is correct. North-West corner method provides a feasible solution that satisfies the supply and demand constraints. However, it may not be the optimal solution.
Statement 3: North-West corner method would yield Vogel's approximate solution.
This statement is incorrect. Vogel's approximation method is a different initial solution method that is based on the difference between the two smallest transportation costs in each row and column of the transportation matrix. It is usually more accurate than the North-West corner method in terms of the total cost.
Conclusion
Therefore, the correct answer is option 'B' - statement 2 alone is correct. North-West corner method provides an initial feasible solution for the transportation problem, but it does not guarantee the optimality of the solution. Other methods are usually used to improve the initial solution and obtain the optimal solution.
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Consider the following statements:In a transportation problem, North-West corner method would yield1. An optimum solution2. An initial feasible solution3. Vogel's app roximat e solutionOf these statements:a)1 alone is correctb)2 alone is correct c)3 alone is correctd)2 and 3 are correctCorrect answer is option 'B'. Can you explain this answer?
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