GATE Linear Programming: Models and Solution Methods – Previous Year Questions

6 GATE previous year questions on Models and Solution Methods (Linear Programming, Mathematics) with answers and explanations, from every paper.

1. GATE 2021 MA Q34 (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,…
2. GATE 2023 MA Q25 (1 mark, Numerical answer) – Minimize 3x₁+4x₂ subject to x₁−x₂≤1,x₁+x₂≥3,x₁,x₂≥0. Find the optimal value.
3. GATE 2024 MA Q25 (1 mark, Multiple choice) – Minimize 5x₁+2x₂ subject to 2x₁+x₂≤2, x₁+x₂≥1, x₁,x₂≥0. Find optimum.
4. GATE 2025 MA Q14 (1 mark, Multiple choice) – Maximize Z=2x₁+4x₂+4x₃−3x₄ with αx₁+x₂+x₃=4, x₁+βx₂+x₄=8, x≥0. S1: for α=2,β=1, (x₁,x₂) is an optimal basis. S2: for α=1,β=4, (x₃,x₂) is an optimal…
5. GATE 2025 MA Q25 (1 mark, Multiple select) – S1=x≥0:2x₁+x₂≤4,x₁+2x₂≤5; S2=x≥0:2x₁−x₂≤5,x₁+2x₂≤5. Which statements hold?
6. GATE 2026 MA Q33 (1 mark, Numerical answer) – Maximize z = 10x₁+20x₂, subject to x₁ ≤ 36, x₂ ≥ 42, x₁+x₂ ≥ 48, 5x₁+x₂ ≤ 150, x₁,x₂ ≥ 0. Find maximum z (integer).