GATE 2021 MA – Question 33
For max 2x₁+3x₂ subject to 2x₁+x₂≤6,−x₁+x₂≤1,x₁+x₂≤3,x₁,x₂≥0, find the optimal value of its dual.
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Correct answer: 8 to 8
Explanation
The feasible point (1,2) gives objective 8. Take (1/2) of the second bound plus (5/2) of the third: 2x₁+3x₂≤1/2+15/2=8. Thus primal optimum is 8. The same multipliers form a feasible dual solution of value 8, confirming by strong duality that the dual optimum is **8**.