GATE 2025 PI – Question 27
A starting simplex tableau maximizes $z=6x_1+4x_2$. Rows list [x₁,x₂,S₁,S₂,S₃,S₄ | RHS]: S₁: [6,3,1,0,0,0 | 36]; S₂: [2,1,0,1,0,0 | 40]; S₃: [−1,3,0,0,1,0 | 2]; S₄: [0,3,0,0,0,1 | 3]. S variables are slacks. Which basic variable leaves?
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Correct answer: (A) $S_1$
Explanation
With initial slack costs zero, x₁ has the largest positive reduced cost, 6, and enters. For positive entries in its column, ratios are 36/6 = 6 and 40/2 = 20. Ignore −1 and 0 entries. Minimum ratio selects **S₁, A**.