The constraints of the given shaded feasible region below of an L.P.P., for non-negative variable constraints x and y are
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(x + y \ge 50, 2x + 5y \lt 200\)
The two lines in the figure, read from their intercepts:
Solid line through (50, 0) and (0, 50): \(x + y = 50\)
Dashed line through (100, 0) and (0, 40): \(2x + 5y = 200\)
The origin test tells which side of each line is shaded:
\(x + y = 50\): the shaded region lies on the side away from O, where \(x + y \ge 50\) (O gives \(0 \lt 50\)).
\(2x + 5y = 200\): the shaded region lies on the same side as O, where \(2x + 5y \lt 200\) (O gives \(0 \lt 200\)).
The line \(2x + 5y = 200\) is drawn dashed, so points on it are not included and the inequality is strict. The solid line \(x + y = 50\) is included.
As a check, the point (60, 10) in the shaded region gives \(60 + 10 = 70 \ge 50\) and \(2(60) + 5(10) = 170 \lt 200\).