GATE 2025 PI – Question 59
Plants P₁,P₂,P₃ supply 6,1,9 thousand litres; centers D₁,D₂,D₃ demand 7,5,4 thousand litres. Transport costs (hundreds of ₹) are P₁: [2,3,11]; P₂: [1,0,6]; P₃: [5,8,15]. Find initial feasible-solution cost using Vogel’s approximation (integer hundreds of ₹).
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Correct answer: 95 to 99
Explanation
Initially D₃ has the largest penalty, 11−6 = 5, so allocate one unit to P₂→D₃. Next D₂ has penalty 8−3 = 5, so allocate five to P₁→D₂. In the remaining table P₃ has penalty 15−5 = 10, so allocate seven to P₃→D₁. Complete with one P₁→D₃ and two P₃→D₃. Total = 1×6 + 5×3 + 7×5 + 1×11 + 2×15 = **97**.