GATE 2026 PI – Question 58
Two oil plants must meet demands of two markets. Costs per litre are C₁₁ = 250, C₁₂ = 280, C₂₁ = 150, C₂₂ = 180; plant capacities K₁ = 500 and K₂ = 600 L; demands D₁ = 300 and D₂ = 400 L. An intern proposes: minimize $Z=\sum_{i=1}^2\sum_{j=1}^2C_{ij}X_{ij}$, subject to $\sum_jX_{ij}\le K_i$ for i = 1,2; $\sum_iX_{ij}\le D_j$ for j = 1,2; and X_ij ≥ 0. Find the optimal objective of the intern’s stated model (integer).
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Correct answer: 0 to 0
Explanation
All costs and quantities are nonnegative, so the objective is at least zero. The stated demand constraints are upper bounds, allowing every shipment to be zero. This feasible choice attains **Z = 0**. The model fails to enforce actual demand satisfaction; correct demand constraints would be equalities or lower bounds, but the question asks about the intern’s model.