GATE 2022 PI – Question 63
Maximize $z=20x_1+6x_2+Px_3$, with C₁: $8x_1+2x_2+3x_3\le250$; C₂: $4x_1+3x_2\le150$; C₃: $2x_1+x_3\le50$; x ≥ 0. Optimal x = (0,50,50) and dual y = (0,2,8). Find P to one decimal.
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Show answer and explanation
Correct answer: 7.9 to 8.1
Explanation
Because x₃ > 0, its dual constraint is tight by complementary slackness. Thus $P=3y_1+0y_2+y_3=0+0+8=\mathbf{8.0}$. As a check, primal value 6×50+8×50 = 700 equals dual value 250×0+150×2+50×8 = 700.