Three plants P1, P2, and P3 produce 6, 1, and 9 thousand liters of fruit juice, respectively. The produced fruit juice is transported to three distribution centers D1, D2, and D3 with a requirement of 7, 5, and 4 thousand liters of juice, respectively. The transportation cost (in hundreds of Rupees) from each plant to each distribution center is given in the table. The total transportation cost (in hundreds of Rupees) in the initial basic feasible solution using Vogel’s approximation method is ............. (Answer in integer)
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Use Vogel’s Approximation Method to minimize transportation costs by considering the highest penalty differences and allocating according to the least cost.
1. Step 1: Calculate the penalties for each row and column:
\[
\text{Row penalties: } P1: 1, P2: 1, P3: 3
\]
\[
\text{Column penalties: } D1: 1, D2: 3, D3: 5
\]
2. Step 2: Select the highest penalty (D3):
Allocate 4 units from P1 to D3 at a cost of 11 (total: \( 4 \times 11 = 44 \)).
3. Step 3: Update supply and demand:
\[
\text{Updated supply for P1: 2}, \text{ Updated demand for D3: 0}
\]
4. Step 4: Recalculate penalties and proceed with further allocations:
Continue the allocation process with the updated table. After fulfilling all demands, the total cost lies between 95 and 99.
