GATE 2022 MA – Question 63

Linear Programming · Duality · 2 marks · Numerical answer

Maximize 6x₁+5x₂ subject to 3x₁+2x₂≤12,−x₁+x₂≤1,x₁,x₂≥0. Find the optimum.

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Correct answer: 27 to 27

Explanation

Multiply the first bound by 11/5 and the second by 3/5. Their sum is 6x₁+5x₂≤132/5+3/5=27. The two boundaries meet at (2,3), a feasible point with objective 12+15=27. Maximum **27**.

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