Mechanical Engineering > GATE 2026 > Linear Programming
An objective function Z of primal variables (x1 and x2) is described below:
Minimize Z = 0.07x1 + 0.05x2
subject to 0.1x1 ≥ 0.4
0.1x2 ≥ 0.6
0.1x1 + 0.2x2 ≥ 2.0
0.2x1 + 0.1x2 ≥ 1.8
x1, x2 ≥ 0
W is the objective function of the dual of Z. k1, k2, k3, and k4 represent the corresponding dual variables.
Which one of the following options represents the correct form of W?
A
Maximize W = 0.4k1+0.6k2+2.0k3+1.8k4 subject to 0.1k1+0.1k3+0.2k4≤0.07, 0.1k2+0.2k3+0.1k4≤0.05
B
Maximize W = 0.4k1+0.6k2+2.0k3+1.8k4 subject to 0.1k1+0.1k2+0.2k4≤0.07, 0.1k2+0.2k3+0.1k4≤0.05
C
Maximize W = 0.4k1+0.6k2+2.0k3+1.8k4 subject to 0.1k1+0.1k2+0.2k4≤0.05, 0.1k1+0.2k3+0.1k4≤0.07
D
Maximize W = 0.4k1+0.6k2+2.0k3+1.8k4 subject to 0.1k1+0.1k3+0.2k4≤0.05, 0.1k2+0.2k3+0.1k4≤0.07

Correct : a

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linear programming dual problem mechanical engineering gate objective function dual primal to dual conversion GATE 2026 Mechanical Engineering linear programming constraints dual variables mechanics optimization mechanics gate

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