Final answer:
The transportation problem is not balanced, and there is an imbalance of 30 units in the supply. To balance the problem, a dummy row or column with a supply of 30 units can be added. Once the problem is balanced, an optimization method can be used to find the minimum cost solution. The correct answer is D.
Step-by-step explanation:
The transportation problem is not balanced because the total supply and total demand are not equal. The total supply is 125 units (20+30+75) and the total demand is 155 units (40+60+55). Therefore, there is an imbalance of 30 units.
The unbalance is in the supply, which means that there is not enough supply to meet the demand. To balance the problem, you can add a dummy row or column with the required amount to make the total supply equal to the total demand. In this case, you would add a dummy row or column with a supply of 30 units.
Once the problem is balanced, you can use an optimization method such as the North-West Corner Method or the Vogel's Approximation Method to find the minimum cost solution.
The transportation problem is not balanced as the total supply of 125 units does not meet the total demand of 155 units; the demand exceeds the supply by 30 units.
To determine if the transportation problem is balanced, we should compare the total supply with the total demand. The total supply is calculated by adding the supply quantities together, which is 20 + 30 + 75 = 125 units. The total demand is found by summing the demand across destinations, which is 40 + 60 + 55 = 155 units.
Since the total supply (125 units) does not equal the total demand (155 units), the transportation problem is not balanced. The unbalance is in the demand which exceeds the supply by 30 units. Once the problem is balanced, an optimization method can be used to find the minimum cost solution.