GATE 2021 MA – Question 34

Linear Programming · Models and Solution Methods · 1 mark · Numerical answer

Minimize 2x₁−5x₂ subject to 2x₁+3x₂+s₁=12,−x₁+x₂+s₂=1,−x₁+2x₂+s₃=3, all five variables nonnegative. If (x₁,2,s₁,s₂,s₃)ᵀ is a basic feasible solution, find x₁+s₁+s₂+s₃.

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Correct answer: 5 to 5

Explanation

With x₂=2, s₁=6−2x₁ and s₂=s₃=x₁−1, so 1≤x₁≤3. A basic solution of three equations in five variables has at least two zero entries. Since x₂>0 and x₁≥1, this forces s₂=s₃=0 and x₁=1; at x₁=3 only s₁ vanishes. Therefore s₁=4,s₂=s₃=0, and the sum is **5**.

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