The minimum value of Z=150 x+200 y for the given constraints aligned & 3 x+5 y 30 & x+y 8 ; x 0, y 0 is aligned

Step-by-step solution

Corner points of the feasible region are found by intersecting the boundary lines. Intersection of 3x + 5y = 30 and x + y = 8 : Subtracting 3(x+y=8) from first: 2y = 6 y = 3, x = 5 . Point: (5, 3) Other corner points: (10, 0) and (0, 8) . Evaluating Z = 150x + 200y : At (10, 0) : Z = 1500 At (5, 3) : Z = 750 + 600 = 1350 At (0, 8) : Z = 1600 Since the feasible region is unbounded, verify that no point in the region gives Z 1350 . The half-plane 150x + 200y Minimum value of Z = 1350 at (5, 3) .