Question

Following information are given for three mines of a company receiving explosives from three suppliers. 

Considering the initial basic feasible solution of this transportation problem, using North-West corner method, the transportation cost of explosives supplied to the company, in Rs., is

• A. 90000
• B. 109000
• C. 293500
• D. 385000

Hint:

In the North-West corner method, start allocating the maximum amount from the top-left corner and move to the next cell, adjusting the supply and demand accordingly.

Answer 1

The Correct Option is B

We are tasked with determining the transportation cost using the North-West corner method for the transportation problem.
Step 1: Apply the North-West corner method
We start by assigning the maximum possible quantities to each cell starting from the top-left corner (i.e., Mine-1 and Supplier-S).
Start with Supplier S and Mine 1. The demand at Mine-1 is 1000 tonnes and Supplier S can supply 2500 tonnes. Therefore, we assign 1000 tonnes to the cell for Supplier S and Mine-1.
The remaining supply at Supplier S is \( 2500 - 1000 = 1500 \) tonnes.
Move to the next column, Mine-2. The demand at Mine-2 is 2000 tonnes, and Supplier S still has 1500 tonnes available. Assign 1500 tonnes to the cell for Supplier S and Mine-2.
The remaining demand at Mine-2 is \( 2000 - 1500 = 500 \) tonnes.
Move to the next column, Mine-3. The demand at Mine-3 is 5000 tonnes, and Supplier S still has 0 tonnes available. We proceed to Supplier O.
The demand at Mine-3 is 5000 tonnes, and Supplier O can supply 2500 tonnes. Assign 2500 tonnes to Supplier O and Mine-3.
The remaining demand at Mine-3 is \( 5000 - 2500 = 2500 \) tonnes.
Finally, move to Supplier I and assign the remaining 2500 tonnes to Supplier I and Mine-3.
Step 2: Calculate the transportation cost
Using the North-West corner method, the quantities assigned are:
Supplier S to Mine-1: 1000 tonnes at Rs. 10/tonne = Rs. 10,000
Supplier S to Mine-2: 1500 tonnes at Rs. 15/tonne = Rs. 22,500
Supplier O to Mine-3: 2500 tonnes at Rs. 100/tonne = Rs. 250,000
Supplier I to Mine-3: 2500 tonnes at Rs. 20/tonne = Rs. 50,000
Total transportation cost is: \[ \text{Total cost} = 10,000 + 22,500 + 250,000 + 50,000 = \mathbf{109,000} \] Conclusion: The total transportation cost of explosives supplied to the company is \( \mathbf{109,000} \, \text{Rs} \).