Concept: Referring to the graphs for given linear equations [ alt="Gate ME GATE 2014 Paper 3 Images Q39" src="//storage.googleapis.com/tb-img/production/15/12/Gate%20ME_GATE%202014%20Paper%203_Images_Q39.PNG" style="height: 251px; width: 328px;"> The constraints x1 ≥ 0, x2 ≥ 0 and x1 + 2x2 ≤ 4 will be having feasible region. The corner points of the feasible region will give the best feasible solution for the objective function. Calculation: Referring to the cornor points of feasible rergion, The corner point of the feasible region are (0, 0), (0, 2) & (4, 0) The value of the objective function at corner points, ⇒ Z (0,0) = 0, ⇒ Z (0,2) = 18 ⇒ Z (4,0) = 12 ∵ The maximum value of Z is at (0, 2) ⇒ Zmax = 18