GATE 2023 MA – Question 65

Linear Programming · Duality · 2 marks · Numerical answer

Maximize 3x₁+2x₂+5x₃ subject to x₁+2x₂+x₃≤44,x₁+2x₃≤48,x₁+4x₂≤52 and x₁,x₂,x₃≥0. Find the optimal value.

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Correct answer: 140 to 140

Explanation

Add the first inequality to twice the second: the left side is exactly 3x₁+2x₂+5x₃, giving upper bound 44+96=140. The point (40,0,4) is feasible: constraint values are 44,48,40, and its objective is 120+20=140. Therefore the maximum is **140**.

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