For the graph of a linear programming problem(LPP) given below. If \( \min z=3x+5y \) is the objective function and shaded portion in the figure is the feasible region of the LPP, then constraints other than \( x,y\ge 0 \) are
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( -2x+y\le 4,x+y\ge 3,x-2y\le 2 \)
For each boundary line, the side of the shaded region is found by testing the origin (0, 0):
−2x + y = 4: the region is on the same side as the origin, and the origin gives 0 ≤ 4, so \( -2x+y\le 4 \).
x + y = 3: the region is on the side away from the origin, and the origin gives 0 < 3, so \( x+y\ge 3 \).
x − 2y = 2: the region is on the same side as the origin, and the origin gives 0 ≤ 2, so \( x-2y\le 2 \).
These are the constraints in Option (3).