GATE 2026 MA – Question 46

Linear Programming · Transportation and Assignment · 2 marks · Multiple choice

Transportation cell costs are c₁₁=10,c₁₂=12,c₂₁=11,c₂₂=13. Multipliers satisfy α₁=x, α₂=x+1, β₁=y, β₂=y+2. Given x=4,c₁₃=19,β₃=y+5, find y and reduced cost d₁₃, using d_ij=c_ij−α_i−β_j.

y=6,d₁₃=7
y=6,d₁₃=4
y=5,d₁₃=7
y=5,d₁₃=4

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Show answer and explanation

Correct answer: (B) y=6,d₁₃=4

Explanation

Basic-cell equalities c_ij = α_i+β_j give 10 = 4+y, hence y = 6, consistently for all four supplied cells. Then β₃ = 11 and d₁₃ = 19−4−11 = 4. **B**.

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