GATE 2026 MA – Question 33
Maximize z = 10x₁+20x₂, subject to x₁ ≤ 36, x₂ ≥ 42, x₁+x₂ ≥ 48, 5x₁+x₂ ≤ 150, x₁,x₂ ≥ 0. Find maximum z (integer).
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Correct answer: 3000 to 3000
Explanation
From x₂ ≤ 150−5x₁, $z\le10x_1+20(150-5x_1)=3000-90x_1\le3000$. The point (0,150) satisfies every constraint and achieves the bound. **Maximum = 3000**.