Question

A vaccine has to be distributed from two warehouses (W1 and W2) to three hospitals (H1, H2, H3). Supplies at W1 and W2 are 200 and 150. Demands at H1, H2, H3 are 100, 150 and 125. Transportation cost (₹ per vaccine) is shown below. Using the Northwest-Corner method, the total transportation cost (₹) is \(\underline{\hspace{2cm}}\) (round off to nearest integer). \[ \begin{array}{c|ccc} & H1 & H2 & H3 \\ \hline W1 & 5 & 7 & 3 \\ W2 & 4 & 6 & 7 \end{array} \]

Hint:

Northwest-Corner always starts at the top-left, filling demand and supply step-by-step before moving right and downward.

Answer 1

Correct Answer: 2190 - 2210

Step 1: Apply Northwest-Corner Allocation. 

Demand: 
H1 = 100, H2 = 150, H3 = 125. 
Supply: 
W1 = 200, W2 = 150.
\(\underline{\text{Cell (W1,H1):}}\) 
Allocate = min(200,100) = 100. 
Remaining: W1 = 100, H1 = 0.
\(\underline{\text{Cell (W1,H2):}}\) 
Allocate = min(100,150) = 100. 
Remaining: W1 = 0, H2 = 50.

\(\underline{\text{Move to W2.}}\)
\(\underline{\text{Cell (W2,H2):}}\) 
Allocate = min(150,50) = 50. 
Remaining: W2 = 100, H2 = 0.
\(\underline{\text{Cell (W2,H3):}}\) 
Allocate = min(100,125) = 100. 
Remaining: W2 = 0, H3 = 25.

Since total supply = 350 < total demand = 375, an additional dummy allocation of 25 to H3 is automatically costed as zero. 

 

Step 2: Compute total cost. \[ C = 100(5) + 100(7) + 50(6) + 100(7) \] \[ = 500 + 700 + 300 + 700 = 2200. \]

Final Answer: \(2200\)